Coverage Report

1		/*
2		* $Id$
3		*
4		* Created on 26 Jan 2010 by Paul Harrison (paul.harrison@manchester.ac.uk)
5		*
6		* Adapted from official SOFA C implementation http://www.iausofa.org/
7		*/
8
9		package org.jastronomy.jsofa;
10
11		import static java.lang.StrictMath.*;
12
13		/**
14		* Java implementation of Standards of Fundamental Astronomy. <a href="http://www.iausofa.org/">http://www.iausofa.org/</a>
15		*
16		* This code has been created by hand translating the official C version.
17		*
18		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 02 Apr 2014
19		* @version JSOFA Release 2016-07-29_a
20		* @since 26 Jan 2010
21		*/
22	0	public class JSOFA {
23		/** tracked IAU SOFA release {@value}. */
24		public final static String SOFA_RELEASE = "2016-07-29";
25
26		/** tracked IAU SOFA revision {@value}. */
27		public final static String SOFA_REVISION = "12";
28
29
30
31		/** Seconds of time to radians {@value} */
32		public final static double DS2R = (7.272205216643039903848712e-5);
33
34		/** Pi {@value}*/
35		public final static double DPI = (3.141592653589793238462643);
36
37		/** 2Pi {@value}*/
38		public final static double D2PI = (6.283185307179586476925287);
39
40		/** Radians to degrees {@value} */
41		public final static double DR2D = (57.29577951308232087679815);
42
43		/** Degrees to radians {@value}*/
44		public final static double DD2R = (1.745329251994329576923691e-2);
45
46		/** Radians to arcseconds {@value}*/
47		public final static double DR2AS = (206264.8062470963551564734);
48
49		/** Arcseconds to radians {@value}*/
50		public final static double DAS2R = (4.848136811095359935899141e-6);
51
52		/** Arcseconds in a full circle {@value}*/
53		public final static double TURNAS = (1296000.0);
54
55		/** Milliarcseconds to radians {@value}*/
56		public final static double DMAS2R = (DAS2R / 1e3);
57
58		/** Length of tropical year B1900 (days) {@value}*/
59		public final static double DTY = (365.242198781);
60
61		/** Reference epoch (J2000.0), Julian Date {@value}*/
62		public final static double DJ00 = (2451545.0);
63
64		/** Julian Date of Modified Julian Date zero {@value}*/
65		public final static double DJM0 = (2400000.5);
66
67		/** Reference epoch (J2000.0), Modified Julian Date {@value} */
68		public final static double DJM00 = (51544.5);
69
70		/** Seconds per day. {@value}*/
71		public final static double DAYSEC = (86400.0);
72
73		/** Days per Julian year */
74		public final static double DJY = (365.25);
75
76		/** Days per Julian century {@value} */
77		public final static double DJC = (36525.0);
78
79		/** Days per Julian millennium {@value} */
80		public final static double DJM = (365250.0);
81
82		/** 1977 Jan 1.0 as MJD */
83		public final static double DJM77 = (43144.0);
84
85		/** TT minus TAI (s) */
86		public final static double TTMTAI = (32.184);
87
88
89		/** Astronomical unit (m) {@value} */
90		public final static double DAU = (149597870e3);
91
92		/** Speed of light (m/s) */
93		public final static double CMPS = 299792458.0;
94
95		/** Light time for 1 au (s) */
96		public final static double AULT = 499.004782;
97
98
99		/** Speed of light (AU per day) {@value} */
100		public final static double DC = (DAYSEC / AULT);
101
102		/** L_G = 1 - d(TT)/d(TCG) */
103		public final static double ELG = (6.969290134e-10);
104
105		/** L_B = 1 - d(TDB)/d(TCB) at TAI 1977/1/1.0 */
106		public final static double ELB = (1.550519768e-8);
107
108		/** Schwarzschild radius of the Sun (au) {@value}
109		= 2 * 1.32712440041e20 / (2.99792458e8)^2 / 1.49597870700e11 */
110		public final static double SRS = 1.97412574336e-8;
111
112
113		/** TDB (s) at TAI 1977/1/1.0 */
114		public final static double TDB0 = (-6.55e-5);
115
116
117		/** dint(A) - truncate to nearest whole number towards zero (double) */
118	24	private static double dint(final double A){ return ((A)<0.0?ceil(A):floor(A));}
119
120		/** dnint(A) - round to nearest whole number (double) */
121	8	private static double dnint(final double A){return ((A)<0.0?ceil((A)-0.5):floor((A)+0.5));}
122
123		/** dsign(A,B) - magnitude of A with sign of B (double) */
124	32	private static double dsign(final double A, double B){return ((B)<0.0?-abs(A):abs(A));}
125
126
127
128		/**
129		* Julian Date representation. The actual date is djm0+djm1, apportioned in any
130		* convenient way between the two arguments. For example,
131		* JD(TT)=2450123.7 could be expressed in any of these ways,
132		* among others:
133		*<pre>
134		* djm0 djm1
135		*
136		* 2450123.7 0.0 (JD method)
137		* 2451545.0 -1421.3 (J2000 method)
138		* 2400000.5 50123.2 (MJD method)
139		* 2450123.5 0.2 (date &time method)
140		*</pre>
141		*
142		* The JD method is the most natural and convenient to use in
143		* cases where the loss of several decimal digits of resolution
144		* is acceptable. The J2000 method is best matched to the way
145		* the argument is handled internally and will deliver the
146		* optimum resolution. The MJD method and the date &time methods
147		* are both good compromises between resolution and convenience.
148		*
149		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Jan 2010
150		*
151		*
152		*/
153		public static class JulianDate {
154		/** MJD zero-point */
155		public double djm0;
156		/** MJD offset */
157		public double djm1;
158	360	public JulianDate(double d1, double d2) {
159	360	djm0 = d1;
160	360	djm1 = d2;
161	360	}
162		}
163
164		/**
165		* Decompose radians into degrees, arcminutes, arcseconds, fraction.
166		*
167		*
168		* <p>This function is derived from the International Astronomical Union's
169		* SOFA (Standards Of Fundamental Astronomy) software collection.
170		*
171		* <p>Status: vector/matrix support function.
172		*
173		*
174		*
175		*<p>Called:<ul>
176		* <li>{@link #jauD2tf} decompose days to hms
177		*</ul>
178		* <p>Notes:
179		*<ol>
180		* <li> The argument ndp is interpreted as follows:
181		*
182		* <pre>
183		* ndp resolution
184		* : ...0000 00 00
185		* -7 1000 00 00
186		* -6 100 00 00
187		* -5 10 00 00
188		* -4 1 00 00
189		* -3 0 10 00
190		* -2 0 01 00
191		* -1 0 00 10
192		* 0 0 00 01
193		* 1 0 00 00.1
194		* 2 0 00 00.01
195		* 3 0 00 00.001
196		* : 0 00 00.000...
197		*</pre>
198		* <li> The largest positive useful value for ndp is determined by the
199		* size of angle, the format of doubles on the target platform, and
200		* the risk of overflowing idmsf[3]. On a typical platform, for
201		* angle up to 2pi, the available floating-point precision might
202		* correspond to ndp=12. However, the practical limit is typically
203		* ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
204		* only 16 bits.
205		*
206		* <li> The absolute value of angle may exceed 2pi. In cases where it
207		* does not, it is up to the caller to test for and handle the
208		* case where angle is very nearly 2pi and rounds up to 360 degrees,
209		* by testing for idmsf[0]=360 and setting idmsf[0-3] to zero.
210		*</ol>
211		*@version 2008 May 27
212		*
213		* @since Release 20101201
214		*
215		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
216		* <!-- Given: -->
217		* @param ndp int resolution (Note 1)
218		* @param angle double angle in radians
219		* @param idmsf int[4] <u>returned</u> degrees, arcminutes, arcseconds, fraction
220		* <!-- Returned: -->
221		* @return sign char '+' or '-'
222		*/
223		public static char jauA2af(final int ndp, final double angle, int idmsf[] ){
224		/* Hours to degrees * radians to turns */
225	2	final double F = 15.0 / D2PI;
226
227
228		/* Scale then use days to h,m,s function. */
229	2	char retval = jauD2tf(ndp, angle*F, idmsf);
230
231	2	return retval;
232
233
234		}
235
236
237
238		/**
239		* Decompose radians into hours, minutes, seconds, fraction.
240		*
241		*<p>This function is derived from the International Astronomical Union's
242		* SOFA (Standards Of Fundamental Astronomy) software collection.
243		*
244		*<p>Status: vector/matrix support function.
245		*
246		*<!-- Given: -->
247		* @param ndp int resolution (Note 1)
248		* @param angle double angle in radians
249		*
250		*<!-- Returned: -->
251		* @param ihmsf int[4] <u>returned</u> hours, minutes, seconds, fraction
252		* @return sign char <u>returned</u> '+' or '-'
253		*
254		*<p>Called:<ul>
255		* <li>{@link #jauD2tf} decompose days to hms
256		* </ul>
257		* <p>Notes:
258		* <ol>
259		*
260		* <li> The argument ndp is interpreted as follows:
261		* <pre>
262		* ndp resolution
263		* : ...0000 00 00
264		* -7 1000 00 00
265		* -6 100 00 00
266		* -5 10 00 00
267		* -4 1 00 00
268		* -3 0 10 00
269		* -2 0 01 00
270		* -1 0 00 10
271		* 0 0 00 01
272		* 1 0 00 00.1
273		* 2 0 00 00.01
274		* 3 0 00 00.001
275		* : 0 00 00.000...
276		*</pre>
277		* <li> The largest positive useful value for ndp is determined by the
278		* size of angle, the format of doubles on the target platform, and
279		* the risk of overflowing ihmsf[3]. On a typical platform, for
280		* angle up to 2pi, the available floating-point precision might
281		* correspond to ndp=12. However, the practical limit is typically
282		* ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
283		* only 16 bits.
284		*
285		* <li> The absolute value of angle may exceed 2pi. In cases where it
286		* does not, it is up to the caller to test for and handle the
287		* case where angle is very nearly 2pi and rounds up to 24 hours,
288		* by testing for ihmsf[0]=24 and setting ihmsf(0-3) to zero.
289		*</ol>
290		* @version 2008 May 11
291		*
292		* @since Release 20101201
293		*
294		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
295		*/
296		public static char jauA2tf(final int ndp, final double angle, int ihmsf[])
297		{
298		/* Scale then use days to h,m,s function. */
299	2	return jauD2tf(ndp, angle/D2PI, ihmsf);
300
301		}
302
303
304		/**
305		* Normalize angle into the range {@literal 0 <= a < 2pi}.
306		*
307		*<p>This function is derived from the International Astronomical Union's
308		* SOFA (Standards Of Fundamental Astronomy) software collection.
309		*
310		*<p>Status: vector/matrix support function.
311		*
312		*<!-- Given: -->
313		* @param a double angle (radians)
314		*
315		* <!-- Returned (function value): -->
316		* @return double angle in range 0-2pi
317		*
318		*@version 2008 May 16
319		*
320		* @since Release 20101201
321		*
322		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
323		*/
324		public static double jauAnp(final double a)
325		{
326		double w;
327
328
329	162	w = fmod(a, D2PI);
330	162	if (w < 0) w += D2PI;
331
332	162	return w;
333
334		}
335
336
337		/**
338		* Normalize angle into the range {@literal -pi <= a < +pi}.
339		*
340		*<p>This function is derived from the International Astronomical Union's
341		* SOFA (Standards Of Fundamental Astronomy) software collection.
342		*
343		*<p>Status: vector/matrix support function.
344		*
345		*<!-- Given: -->
346		* @param a double angle (radians)
347		*
348		* <!-- Returned (function value): -->
349		* @return double angle in range +/-pi
350		*
351		*@version 2008 May 16
352		*
353		* @since Release 20101201
354		*
355		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
356		*/
357		public static double jauAnpm(final double a)
358		{
359		double w;
360
361
362	78	w = fmod(a, D2PI);
363	78	if (abs(w) >= DPI) w -= dsign(D2PI, a);
364
365	78	return w;
366
367		}
368		/**
369		* Frame bias components of IAU 2000 precession-nutation models.
370		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 2 Feb 2010
371		*
372		* @since AIDA Stage 1
373		*/
374	38	public static class FrameBias {
375		/** longitude corrections */
376		public double dpsibi;
377		/*obliquity corrections /
378		public double depsbi;
379		/** the ICRS RA of the J2000.0 mean equinox */
380		public double dra;
381		};
382
383		/**
384		* Frame bias components of IAU 2000 precession-nutation models (part
385		* of MHB2000 with additions).
386		*
387		*<p>This function is derived from the International Astronomical Union's
388		* SOFA (Standards Of Fundamental Astronomy) software collection.
389		*
390		*<p>Status: canonical model.
391		*
392		*<!-- Returned: -->
393		* @return dpsibi,depsbi double <u>returned</u> longitude and obliquity corrections
394		* dra double <u>returned</u> the ICRS RA of the J2000.0 mean equinox
395		*
396		* <p>Notes:
397		* <ol>
398		*
399		* <li> The frame bias corrections in longitude and obliquity (radians)
400		* are required in order to correct for the offset between the GCRS
401		* pole and the mean J2000.0 pole. They define, with respect to the
402		* GCRS frame, a J2000.0 mean pole that is consistent with the rest
403		* of the IAU 2000A precession-nutation model.
404		*
405		* <li> In addition to the displacement of the pole, the complete
406		* description of the frame bias requires also an offset in right
407		* ascension. This is not part of the IAU 2000A model, and is from
408		* Chapront et al. (2002). It is returned in radians.
409		*
410		* <li> This is a supplemented implementation of one aspect of the IAU
411		* 2000A nutation model, formally adopted by the IAU General
412		* Assembly in 2000, namely MHB2000 (Mathews et al. 2002).
413		*</ol>
414		*<p>References:
415		*
416		* Chapront, J., Chapront-Touze, M. &Francou, G., Astron.
417		* Astrophys., 387, 700, 2002.
418		*
419		* <p>Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
420		* and precession New nutation series for nonrigid Earth and
421		* insights into the Earth's interior", J.Geophys.Res., 107, B4,
422		* 2002. The MHB2000 code itself was obtained on 9th September 2002
423		* from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
424		*
425		*@version 2009 December 17
426		*
427		* @since Release 20101201
428		*
429		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
430		*/
431		public static FrameBias jauBi00()
432		{
433		/* The frame bias corrections in longitude and obliquity */
434	38	final double DPBIAS = -0.041775 * DAS2R,
435	38	DEBIAS = -0.0068192 * DAS2R;
436
437		/* The ICRS RA of the J2000.0 equinox (Chapront et al., 2002) */
438	38	final double DRA0 = -0.0146 * DAS2R;
439
440
441		/* Return the results (which are fixed). */
442	38	FrameBias retval = new FrameBias();
443	38	retval.dpsibi = DPBIAS;
444	38	retval.depsbi = DEBIAS;
445	38	retval.dra = DRA0;
446
447	38	return retval;
448
449		}
450
451
452		/**
453		* Frame bias and precession, IAU 2000.
454		*
455		*<p>This function is derived from the International Astronomical Union's
456		* SOFA (Standards Of Fundamental Astronomy) software collection.
457		*
458		*<p>Status: canonical model.
459		*
460		*<!-- Given: -->
461		* @param date1
462		* @param date2 double TT as a 2-part Julian Date (Note 1)
463		*
464		*<!-- Returned: -->
465		* @param rb double[3][3] <u>returned</u> frame bias matrix (Note 2)
466		* @param rp double[3][3] <u>returned</u> precession matrix (Note 3)
467		* @param rbp double[3][3] <u>returned</u> bias-precession matrix (Note 4)
468		*
469		* <p>Notes:
470		* <ol>
471		*
472		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
473		* convenient way between the two arguments. For example,
474		* JD(TT)=2450123.7 could be expressed in any of these ways,
475		* among others:
476		*<pre>
477		* date1 date2
478		*
479		* 2450123.7 0.0 (JD method)
480		* 2451545.0 -1421.3 (J2000 method)
481		* 2400000.5 50123.2 (MJD method)
482		* 2450123.5 0.2 (date &time method)
483		*</pre>
484		* The JD method is the most natural and convenient to use in
485		* cases where the loss of several decimal digits of resolution
486		* is acceptable. The J2000 method is best matched to the way
487		* the argument is handled internally and will deliver the
488		* optimum resolution. The MJD method and the date &time methods
489		* are both good compromises between resolution and convenience.
490		*
491		* <li> The matrix rb transforms vectors from GCRS to mean J2000.0 by
492		* applying frame bias.
493		*
494		* <li> The matrix rp transforms vectors from J2000.0 mean equator and
495		* equinox to mean equator and equinox of date by applying
496		* precession.
497		*
498		* <li> The matrix rbp transforms vectors from GCRS to mean equator and
499		* equinox of date by applying frame bias then precession. It is
500		* the product rp x rb.
501		*
502		* <li> It is permissible to re-use the same array in the returned
503		* arguments. The arrays are filled in the order given.
504		*</ol>
505		*<p>Called:<ul>
506		* <li>{@link #jauBi00} frame bias components, IAU 2000
507		* <li>{@link #jauPr00} IAU 2000 precession adjustments
508		* <li>{@link #jauIr} initialize r-matrix to identity
509		* <li>{@link #jauRx} rotate around X-axis
510		* <li>{@link #jauRy} rotate around Y-axis
511		* <li>{@link #jauRz} rotate around Z-axis
512		* <li>{@link #jauCr} copy r-matrix
513		* <li>{@link #jauRxr} product of two r-matrices
514		* </ul>
515		*<p>Reference:
516		* "Expressions for the Celestial Intermediate Pole and Celestial
517		* Ephemeris Origin consistent with the IAU 2000A precession-
518		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
519		*
520		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
521		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
522		*
523		*@version 2010 January 18
524		*
525		* @since Release 20101201
526		*
527		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
528		*/
529		public static void jauBp00(final double date1, final double date2,
530		double rb[][], double rp[][], double rbp[][])
531		{
532		/* J2000.0 obliquity (Lieske et al. 1977) */
533	36	final double EPS0 = 84381.448 * DAS2R;
534
535		double t, dpsibi, depsbi;
536		double dra0, psia77, oma77, chia, dpsipr, depspr, psia, oma,
537	36	rbw[][] = new double[3][3];
538
539
540		/* Interval between fundamental epoch J2000.0 and current date (JC). */
541	36	t = ((date1 - DJ00) + date2) / DJC;
542
543		/* Frame bias. */
544	36	FrameBias fb = jauBi00();
545	36	dpsibi = fb.dpsibi;
546	36	depsbi = fb.depsbi;
547	36	dra0 = fb.dra;
548		/* Precession angles (Lieske et al. 1977) */
549	36	psia77 = (5038.7784 + (-1.07259 + (-0.001147) * t) * t) * t * DAS2R;
550	36	oma77 = EPS0 + ((0.05127 + (-0.007726) * t) * t) * t * DAS2R;
551	36	chia = ( 10.5526 + (-2.38064 + (-0.001125) * t) * t) * t * DAS2R;
552
553		/* Apply IAU 2000 precession corrections. */
554	36	PrecessionDeltaTerms pc = jauPr00(date1, date2);
555	36	dpsipr = pc.dpsipr; depspr = pc.depspr;
556	36	psia = psia77 + dpsipr;
557	36	oma = oma77 + depspr;
558
559		/* Frame bias matrix: GCRS to J2000.0. */
560	36	jauIr(rbw);
561	36	jauRz(dra0, rbw);
562	36	jauRy(dpsibi * sin(EPS0), rbw);
563	36	jauRx(-depsbi, rbw);
564	36	jauCr(rbw, rb);
565
566		/* Precession matrix: J2000.0 to mean of date. */
567	36	jauIr(rp);
568	36	jauRx(EPS0, rp);
569	36	jauRz(-psia, rp);
570	36	jauRx(-oma, rp);
571	36	jauRz(chia, rp);
572
573		/* Bias-precession matrix: GCRS to mean of date. */
574	36	double[][] rt = jauRxr(rp, rbw );
575	36	jauCr(rt, rbp);
576	36	return;
577
578		}
579
580
581		/**
582		* Frame bias and precession, IAU 2006.
583		*
584		*<p>This function is derived from the International Astronomical Union's
585		* SOFA (Standards Of Fundamental Astronomy) software collection.
586		*
587		*<p>Status: support function.
588		*
589		*<!-- Given: -->
590		* @param date1 double TT as a 2-part Julian Date (Note 1)
591		* @param date2 double TT as a 2-part Julian Date (Note 1)
592		*
593		*<!-- Returned: -->
594		* @param rb double[3][3] <u>returned</u> frame bias matrix (Note 2)
595		* @param rp double[3][3] <u>returned</u> precession matrix (Note 3)
596		* @param rbp double[3][3] <u>returned</u> bias-precession matrix (Note 4)
597		*
598		* <p>Notes:
599		* <ol>
600		*
601		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
602		* convenient way between the two arguments. For example,
603		* JD(TT)=2450123.7 could be expressed in any of these ways,
604		* among others:
605		*<pre>
606		* date1 date2
607		*
608		* 2450123.7 0.0 (JD method)
609		* 2451545.0 -1421.3 (J2000 method)
610		* 2400000.5 50123.2 (MJD method)
611		* 2450123.5 0.2 (date &time method)
612		*</pre>
613		* The JD method is the most natural and convenient to use in
614		* cases where the loss of several decimal digits of resolution
615		* is acceptable. The J2000 method is best matched to the way
616		* the argument is handled internally and will deliver the
617		* optimum resolution. The MJD method and the date &time methods
618		* are both good compromises between resolution and convenience.
619		*
620		* <li> The matrix rb transforms vectors from GCRS to mean J2000.0 by
621		* applying frame bias.
622		*
623		* <li> The matrix rp transforms vectors from mean J2000.0 to mean of
624		* date by applying precession.
625		*
626		* <li> The matrix rbp transforms vectors from GCRS to mean of date by
627		* applying frame bias then precession. It is the product rp x rb.
628		*
629		* <li> It is permissible to re-use the same array in the returned
630		* arguments. The arrays are filled in the order given.
631		*</ol>
632		*<p>Called:<ul>
633		* <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
634		* <li>{@link #jauFw2m} F-W angles to r-matrix
635		* <li>{@link #jauPmat06} PB matrix, IAU 2006
636		* <li>{@link #jauTr} transpose r-matrix
637		* <li>{@link #jauRxr} product of two r-matrices
638		* </ul>
639		*<p>References:
640		*
641		* <p>Capitaine, N. &Wallace, P.T., 2006, Astron.Astrophys. 450, 855
642		*
643		* <p>Wallace, P.T. &Capitaine, N., 2006, Astron.Astrophys. 459, 981
644		*
645		*@version 2009 December 17
646		*
647		* @since Release 20101201
648		*
649		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
650		*/
651		public static void jauBp06(final double date1, final double date2,
652		double rb[][], double rp[][], double rbp[][])
653		{
654		double rbt[][];
655
656
657		/* B matrix. */
658	2	FWPrecessionAngles fw = jauPfw06(DJM0, DJM00);
659	2	double[][] rt = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa);
660	2	jauCr(rt, rb);
661
662		/* PxB matrix. */
663	2	rt = jauPmat06(date1, date2 );
664	2	jauCr(rt, rbp);
665
666		/* P matrix. */
667	2	rbt = jauTr(rb);
668	2	rt = jauRxr(rbp, rbt);
669	2	jauCr(rt, rp);
670
671	2	return;
672
673		}
674
675		/**
676		* The components x,y are components of the Celestial Intermediate
677		* Pole unit vector in the Geocentric Celestial Reference System.
678		*
679		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 29 Jan 2010
680		*
681		* @since AIDA Stage 1
682		*/
683		public static class CelestialIntermediatePole {
684		public double x;
685		public double y;
686	66	public CelestialIntermediatePole(double x, double y) {
687	66	this.x = x;
688	66	this.y = y;
689	66	}
690		}
691		/**
692		* Extract from the bias-precession-nutation matrix the X,Y coordinates
693		* of the Celestial Intermediate Pole.
694		*
695		*<p>This function is derived from the International Astronomical Union's
696		* SOFA (Standards Of Fundamental Astronomy) software collection.
697		*
698		*<p>Status: support function.
699		*
700		*<!-- Given: -->
701		* @param rbpn double[3][3] celestial-to-true matrix (Note 1)
702		*
703		*<!-- Returned: -->
704		* @return <u>returned</u> Celestial Intermediate Pole (Note 2)
705		*
706		* <p>Notes:
707		* <ol>
708		*
709		* <li> The matrix rbpn transforms vectors from GCRS to true equator (and
710		* CIO or equinox) of date, and therefore the Celestial Intermediate
711		* Pole unit vector is the bottom row of the matrix.
712		*
713		* <li> The arguments x,y are components of the Celestial Intermediate
714		* Pole unit vector in the Geocentric Celestial Reference System.
715		*</ol>
716		*<p>Reference:
717		*
718		* "Expressions for the Celestial Intermediate Pole and Celestial
719		* Ephemeris Origin consistent with the IAU 2000A precession-
720		* nutation model", Astron.Astrophys. 400, 1145-1154
721		* (2003)
722		*
723		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
724		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
725		*
726		*@version 2010 January 18
727		*
728		* @since Release 20101201
729		*
730		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
731		*/
732		public static CelestialIntermediatePole jauBpn2xy(double rbpn[][])
733		{
734		/* Extract the X,Y coordinates. */
735
736	64	return new CelestialIntermediatePole(rbpn[2][0], rbpn[2][1]);
737
738		}
739
740
741		/**
742		* Form the celestial-to-intermediate matrix for a given date using the
743		* IAU 2000A precession-nutation model.
744		*
745		*<p>This function is derived from the International Astronomical Union's
746		* SOFA (Standards Of Fundamental Astronomy) software collection.
747		*
748		*<p>Status: support function.
749		*
750		*<!-- Given: -->
751		* @param date1 double TT as a 2-part Julian Date (Note 1)
752		* @param date2 double TT as a 2-part Julian Date (Note 1)
753		*
754		*<!-- Returned: -->
755		* @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 2)
756		*
757		* <p>Notes:
758		* <ol>
759		*
760		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
761		* convenient way between the two arguments. For example,
762		* JD(TT)=2450123.7 could be expressed in any of these ways,
763		* among others:
764		*<pre>
765		* date1 date2
766		*
767		* 2450123.7 0.0 (JD method)
768		* 2451545.0 -1421.3 (J2000 method)
769		* 2400000.5 50123.2 (MJD method)
770		* 2450123.5 0.2 (date &time method)
771		*</pre>
772		* The JD method is the most natural and convenient to use in
773		* cases where the loss of several decimal digits of resolution
774		* is acceptable. The J2000 method is best matched to the way
775		* the argument is handled internally and will deliver the
776		* optimum resolution. The MJD method and the date &time methods
777		* are both good compromises between resolution and convenience.
778		*
779		* <li> The matrix rc2i is the first stage in the transformation from
780		* celestial to terrestrial coordinates:
781		*
782		* [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
783		*
784		* = rc2t * [CRS]
785		*
786		* where [CRS] is a vector in the Geocentric Celestial Reference
787		* System and [TRS] is a vector in the International Terrestrial
788		* Reference System (see IERS Conventions 2003), ERA is the Earth
789		* Rotation Angle and RPOM is the polar motion matrix.
790		*
791		* <li> A faster, but slightly less accurate result (about 1 mas), can be
792		* obtained by using instead the jauC2i00b function.
793		*</ol>
794		*<p>Called:<ul>
795		* <li>{@link #jauPnm00a} classical NPB matrix, IAU 2000A
796		* <li>{@link #jauC2ibpn} celestial-to-intermediate matrix, given NPB matrix
797		* </ul>
798		*<p>References:
799		*<ul>
800		* <li>"Expressions for the Celestial Intermediate Pole and Celestial
801		* Ephemeris Origin consistent with the IAU 2000A precession-
802		* nutation model", Astron.Astrophys. 400, 1145-1154
803		* (2003)
804		*
805		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
806		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
807		*
808		* <li>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
809		* IERS Technical Note No. 32, BKG (2004)
810		*</ul>
811		*@version 2010 January 18
812		*
813		* @since Release 20101201
814		*
815		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
816		*/
817		public static double[][] jauC2i00a(double date1, double date2)
818		{
819
820
821		/* Obtain the celestial-to-true matrix (IAU 2000A). */
822	4	double rbpn[][] = jauPnm00a(date1, date2);
823
824		/* Form the celestial-to-intermediate matrix. */
825	4	double rc2i[][] =jauC2ibpn(date1, date2, rbpn);
826
827	4	return rc2i;
828
829		}
830
831
832		/**
833		* Form the celestial-to-intermediate matrix for a given date using the
834		* IAU 2000B precession-nutation model.
835		*
836		*<p>This function is derived from the International Astronomical Union's
837		* SOFA (Standards Of Fundamental Astronomy) software collection.
838		*
839		*<p>Status: support function.
840		*
841		*<!-- Given: -->
842		* @param date1 double TT as a 2-part Julian Date (Note 1)
843		* @param date2 double TT as a 2-part Julian Date (Note 1)
844		*
845		*<!-- Returned: -->
846		* @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 2)
847		*
848		* <p>Notes:
849		* <ol>
850		*
851		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
852		* convenient way between the two arguments. For example,
853		* JD(TT)=2450123.7 could be expressed in any of these ways,
854		* among others:
855		*<pre>
856		* date1 date2
857		*
858		* 2450123.7 0.0 (JD method)
859		* 2451545.0 -1421.3 (J2000 method)
860		* 2400000.5 50123.2 (MJD method)
861		* 2450123.5 0.2 (date &time method)
862		*</pre>
863		* The JD method is the most natural and convenient to use in
864		* cases where the loss of several decimal digits of resolution
865		* is acceptable. The J2000 method is best matched to the way
866		* the argument is handled internally and will deliver the
867		* optimum resolution. The MJD method and the date &time methods
868		* are both good compromises between resolution and convenience.
869		*
870		* <li> The matrix rc2i is the first stage in the transformation from
871		* celestial to terrestrial coordinates:
872		*
873		* [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
874		*
875		* = rc2t * [CRS]
876		*
877		* where [CRS] is a vector in the Geocentric Celestial Reference
878		* System and [TRS] is a vector in the International Terrestrial
879		* Reference System (see IERS Conventions 2003), ERA is the Earth
880		* Rotation Angle and RPOM is the polar motion matrix.
881		*
882		* <li> The present function is faster, but slightly less accurate (about
883		* 1 mas), than the jauC2i00a function.
884		*</ol>
885		*<p>Called:<ul>
886		* <li>{@link #jauPnm00b} classical NPB matrix, IAU 2000B
887		* <li>{@link #jauC2ibpn} celestial-to-intermediate matrix, given NPB matrix
888		* </ul>
889		*<p>References:
890		*
891		* <p> "Expressions for the Celestial Intermediate Pole and Celestial
892		* Ephemeris Origin consistent with the IAU 2000A precession-
893		* nutation model", Astron.Astrophys. 400, 1145-1154
894		* (2003)
895		*
896		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
897		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
898		*
899		* <p> McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
900		* IERS Technical Note No. 32, BKG (2004)
901		*
902		*@version 2010 January 18
903		*
904		* @since Release 20101201
905		*
906		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
907		*/
908		public static double[][] jauC2i00b(double date1, double date2)
909		{
910		double rbpn[][];
911		double rc2i[][];
912
913		/* Obtain the celestial-to-true matrix (IAU 2000B). */
914	4	rbpn = jauPnm00b(date1, date2 );
915
916		/* Form the celestial-to-intermediate matrix. */
917	4	rc2i = jauC2ibpn(date1, date2, rbpn);
918
919	4	return rc2i;
920
921		}
922
923
924		/**
925		* Form the celestial-to-intermediate matrix for a given date using the
926		* IAU 2006 precession and IAU 2000A nutation models.
927		*
928		*<p>This function is derived from the International Astronomical Union's
929		* SOFA (Standards Of Fundamental Astronomy) software collection.
930		*
931		*<p>Status: support function.
932		*
933		*<!-- Given: -->
934		* @param date1 double TT as a 2-part Julian Date (Note 1)
935		* @param date2 double TT as a 2-part Julian Date (Note 1)
936		*
937		*<!-- Returned: -->
938		* @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 2)
939		*
940		* <p>Notes:
941		* <ol>
942		*
943		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
944		* convenient way between the two arguments. For example,
945		* JD(TT)=2450123.7 could be expressed in any of these ways,
946		* among others:
947		*<pre>
948		* date1 date2
949		*
950		* 2450123.7 0.0 (JD method)
951		* 2451545.0 -1421.3 (J2000 method)
952		* 2400000.5 50123.2 (MJD method)
953		* 2450123.5 0.2 (date &time method)
954		*</pre>
955		* The JD method is the most natural and convenient to use in
956		* cases where the loss of several decimal digits of resolution
957		* is acceptable. The J2000 method is best matched to the way
958		* the argument is handled internally and will deliver the
959		* optimum resolution. The MJD method and the date &time methods
960		* are both good compromises between resolution and convenience.
961		*
962		* <li> The matrix rc2i is the first stage in the transformation from
963		* celestial to terrestrial coordinates:
964		*
965		* [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
966		*
967		* = RC2T * [CRS]
968		*
969		* where [CRS] is a vector in the Geocentric Celestial Reference
970		* System and [TRS] is a vector in the International Terrestrial
971		* Reference System (see IERS Conventions 2003), ERA is the Earth
972		* Rotation Angle and RPOM is the polar motion matrix.
973		*</ol>
974		*<p>Called:<ul>
975		* <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
976		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
977		* <li>{@link #jauS06} the CIO locator s, Given X,Y, IAU 2006
978		* <li>{@link #jauC2ixys} celestial-to-intermediate matrix, Given X,Y and s
979		* </ul>
980		*<p>References:
981		*
982		* <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
983		* IERS Technical Note No. 32, BKG
984		*
985		*@version 2008 May 13
986		*
987		* @since Release 20101201
988		*
989		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
990		*/
991		public static double[][] jauC2i06a(double date1, double date2)
992		{
993		double rbpn[][], s, rc2i[][];
994
995
996		/* Obtain the celestial-to-true matrix (IAU 2006/2000A). */
997	4	rbpn = jauPnm06a(date1, date2);
998
999		/* Extract the X,Y coordinates. */
1000	4	CelestialIntermediatePole cip = jauBpn2xy(rbpn);
1001
1002		/* Obtain the CIO locator. */
1003	4	s = jauS06(date1, date2, cip.x, cip.y);
1004
1005		/* Form the celestial-to-intermediate matrix. */
1006	4	rc2i = jauC2ixys(cip.x, cip.y, s);
1007
1008	4	return rc2i;
1009
1010		}
1011
1012
1013		/**
1014		* Form the celestial-to-intermediate matrix for a given date given
1015		* the bias-precession-nutation matrix. IAU 2000.
1016		*
1017		*<p>This function is derived from the International Astronomical Union's
1018		* SOFA (Standards Of Fundamental Astronomy) software collection.
1019		*
1020		*<p>Status: support function.
1021		*
1022		*<!-- Given: -->
1023		* @param date1 double TT as a 2-part Julian Date (Note 1)
1024		* @param date2 double TT as a 2-part Julian Date (Note 1)
1025		* @param rbpn double[3][3] celestial-to-true matrix (Note 2)
1026		*
1027		*<!-- Returned: -->
1028		* @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 3)
1029		*
1030		* <p>Notes:
1031		* <ol>
1032		*
1033		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
1034		* convenient way between the two arguments. For example,
1035		* JD(TT)=2450123.7 could be expressed in any of these ways,
1036		* among others:
1037		*<pre>
1038		* date1 date2
1039		*
1040		* 2450123.7 0.0 (JD method)
1041		* 2451545.0 -1421.3 (J2000 method)
1042		* 2400000.5 50123.2 (MJD method)
1043		* 2450123.5 0.2 (date &time method)
1044		*</pre>
1045		* The JD method is the most natural and convenient to use in
1046		* cases where the loss of several decimal digits of resolution
1047		* is acceptable. The J2000 method is best matched to the way
1048		* the argument is handled internally and will deliver the
1049		* optimum resolution. The MJD method and the date &time methods
1050		* are both good compromises between resolution and convenience.
1051		*
1052		* <li> The matrix rbpn transforms vectors from GCRS to true equator (and
1053		* CIO or equinox) of date. Only the CIP (bottom row) is used.
1054		*
1055		* <li> The matrix rc2i is the first stage in the transformation from
1056		* celestial to terrestrial coordinates:
1057		*
1058		* [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1059		*
1060		* = RC2T * [CRS]
1061		*
1062		* where [CRS] is a vector in the Geocentric Celestial Reference
1063		* System and [TRS] is a vector in the International Terrestrial
1064		* Reference System (see IERS Conventions 2003), ERA is the Earth
1065		* Rotation Angle and RPOM is the polar motion matrix.
1066		*
1067		* <li> Although its name does not include "00", This function is in fact
1068		* specific to the IAU 2000 models.
1069		*</ol>
1070		*<p>Called:<ul>
1071		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
1072		* <li>{@link #jauC2ixy} celestial-to-intermediate matrix, given X,Y
1073		* </ul>
1074		*<p>References:
1075		* <p> "Expressions for the Celestial Intermediate Pole and Celestial
1076		* Ephemeris Origin consistent with the IAU 2000A precession-
1077		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
1078		*
1079		* <p>n.b. The celestial ephemeris origin (CEO) was renamed "celestial
1080		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
1081		*
1082		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1083		* IERS Technical Note No. 32, BKG (2004)
1084		*
1085		*@version 2010 January 18
1086		*
1087		* @since Release 20101201
1088		*
1089		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1090		*/
1091		public static double[][] jauC2ibpn(double date1, double date2, double rbpn[][])
1092		{
1093
1094		/* Extract the X,Y coordinates. */
1095	10	CelestialIntermediatePole cip = jauBpn2xy(rbpn);
1096
1097
1098		/* Form the celestial-to-intermediate matrix (n.b. IAU 2000 specific). */
1099	10	double rc2i[][] =jauC2ixy(date1, date2, cip.x, cip.y);
1100
1101	10	return rc2i;
1102
1103		}
1104
1105
1106		/**
1107		* Form the celestial to intermediate-frame-of-date matrix for a given
1108		* date when the CIP X,Y coordinates are known. IAU 2000.
1109		*
1110		*<p>This function is derived from the International Astronomical Union's
1111		* SOFA (Standards Of Fundamental Astronomy) software collection.
1112		*
1113		*<p>Status: support function.
1114		*
1115		*<!-- Given: -->
1116		* @param date1 double TT as a 2-part Julian Date (Note 1)
1117		* @param date2 double TT as a 2-part Julian Date (Note 1)
1118		* @param x double Celestial Intermediate Pole (Note 2)
1119		* @param y double Celestial Intermediate Pole (Note 2)
1120		*
1121		*<!-- Returned: -->
1122		* @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 3)
1123		*
1124		* <p>Notes:
1125		* <ol>
1126		*
1127		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
1128		* convenient way between the two arguments. For example,
1129		* JD(TT)=2450123.7 could be expressed in any of these ways,
1130		* among others:
1131		*<pre>
1132		* date1 date2
1133		*
1134		* 2450123.7 0.0 (JD method)
1135		* 2451545.0 -1421.3 (J2000 method)
1136		* 2400000.5 50123.2 (MJD method)
1137		* 2450123.5 0.2 (date &time method)
1138		*</pre>
1139		* The JD method is the most natural and convenient to use in
1140		* cases where the loss of several decimal digits of resolution
1141		* is acceptable. The J2000 method is best matched to the way
1142		* the argument is handled internally and will deliver the
1143		* optimum resolution. The MJD method and the date &time methods
1144		* are both good compromises between resolution and convenience.
1145		*
1146		* <li> The Celestial Intermediate Pole coordinates are the x,y components
1147		* of the unit vector in the Geocentric Celestial Reference System.
1148		*
1149		* <li> The matrix rc2i is the first stage in the transformation from
1150		* celestial to terrestrial coordinates:
1151		*
1152		* [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1153		*
1154		* = RC2T * [CRS]
1155		*
1156		* where [CRS] is a vector in the Geocentric Celestial Reference
1157		* System and [TRS] is a vector in the International Terrestrial
1158		* Reference System (see IERS Conventions 2003), ERA is the Earth
1159		* Rotation Angle and RPOM is the polar motion matrix.
1160		*
1161		* <li> Although its name does not include "00", This function is in fact
1162		* specific to the IAU 2000 models.
1163		*</ol>
1164		*<p>Called:<ul>
1165		* <li>{@link #jauC2ixys} celestial-to-intermediate matrix, given X,Y and s
1166		* <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
1167		* </ul>
1168		*<p>Reference:
1169		*
1170		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1171		* IERS Technical Note No. 32, BKG (2004)
1172		*
1173		*@version 2008 May 11
1174		*
1175		* @since Release 20101201
1176		*
1177		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1178		*/
1179
1180		public static double[][] jauC2ixy(double date1, double date2, double x, double y)
1181		{
1182		/* Compute s and then the matrix. */
1183	14	double rc2i[][] = jauC2ixys(x, y, jauS00(date1, date2, x, y));
1184
1185	14	return rc2i;
1186
1187		}
1188
1189
1190		/**
1191		* Form the celestial to intermediate-frame-of-date matrix given the CIP
1192		* X,Y and the CIO locator s.
1193		*
1194		*<p>This function is derived from the International Astronomical Union's
1195		* SOFA (Standards Of Fundamental Astronomy) software collection.
1196		*
1197		*<p>Status: support function.
1198		*
1199		*<!-- Given: -->
1200		* @param x double Celestial Intermediate Pole (Note 1)
1201		* @param y double Celestial Intermediate Pole (Note 1)
1202		* @param s double the CIO locator s (Note 2)
1203		*
1204		*<!-- Returned: -->
1205		* @return rc2i double[3][3] <u>returned</u> celestial-to-intermediate matrix (Note 3)
1206		*
1207		* <p>Notes:
1208		* <ol>
1209		*
1210		* <li> The Celestial Intermediate Pole coordinates are the x,y
1211		* components of the unit vector in the Geocentric Celestial
1212		* Reference System.
1213		*
1214		* <li> The CIO locator s (in radians) positions the Celestial
1215		* Intermediate Origin on the equator of the CIP.
1216		*
1217		* <li> The matrix rc2i is the first stage in the transformation from
1218		* celestial to terrestrial coordinates:
1219		*
1220		* [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1221		*
1222		* = RC2T * [CRS]
1223		*
1224		* where [CRS] is a vector in the Geocentric Celestial Reference
1225		* System and [TRS] is a vector in the International Terrestrial
1226		* Reference System (see IERS Conventions 2003), ERA is the Earth
1227		* Rotation Angle and RPOM is the polar motion matrix.
1228		*</ol>
1229		*<p>Called:<ul>
1230		* <li>{@link #jauIr} initialize r-matrix to identity
1231		* <li>{@link #jauRz} rotate around Z-axis
1232		* <li>{@link #jauRy} rotate around Y-axis
1233		* </ul>
1234		*<p>Reference:
1235		*
1236		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1237		* IERS Technical Note No. 32, BKG (2004)
1238		*
1239		*@version 2008 May 11
1240		*
1241		* @since Release 20101201
1242		*
1243		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1244		*/
1245		public static double[][] jauC2ixys(double x, double y, double s)
1246		{
1247		double r2, e, d;
1248	50	double rc2i[][] = new double[3][3];
1249
1250		/* Obtain the spherical angles E and d. */
1251	50	r2 = xx + yy;
1252	50	e = (r2 > 0.0) ? atan2(y, x) : 0.0;
1253	50	d = atan(sqrt(r2 / (1.0 - r2)));
1254
1255		/* Form the matrix. */
1256	50	jauIr(rc2i);
1257	50	jauRz(e, rc2i);
1258	50	jauRy(d, rc2i);
1259	50	jauRz(-(e+s), rc2i);
1260
1261	50	return rc2i;
1262
1263		}
1264
1265		/**
1266		* P-vector to spherical coordinates.
1267		*
1268		*<p>This function is derived from the International Astronomical Union's
1269		* SOFA (Standards Of Fundamental Astronomy) software collection.
1270		*
1271		*<p>Status: vector/matrix support function.
1272		*
1273		*<!-- Given: -->
1274		* @param p double[3] p-vector
1275		*
1276		*<!-- Returned: -->
1277		* @return theta double <u>returned</u> longitude angle (radians)
1278		* phi double <u>returned</u> latitude angle (radians)
1279		*
1280		* <p>Notes:
1281		* <ol>
1282		*
1283		* <li> The vector p can have any magnitude; only its direction is used.
1284		*
1285		* <li> If p is null, zero theta and phi are returned.
1286		*
1287		* <li> At either pole, zero theta is returned.
1288		*</ol>
1289		*@version 2008 May 11
1290		*
1291		* @since Release 20101201
1292		*
1293		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1294		*/
1295		public static SphericalCoordinate jauC2s(double p[])
1296		{
1297		double x, y, z, d2;
1298
1299
1300	64	x = p[0];
1301	64	y = p[1];
1302	64	z = p[2];
1303	64	d2 = xx + yy;
1304
1305	64	double theta = (d2 == 0.0) ? 0.0 : atan2(y, x);
1306	64	double phi = (z == 0.0) ? 0.0 : atan2(z, sqrt(d2));
1307
1308	64	return new SphericalCoordinate(theta, phi);
1309
1310		}
1311
1312
1313		/**
1314		* Form the celestial to terrestrial matrix given the date, the UT1 and
1315		* the polar motion, using the IAU 2000A nutation model.
1316		*
1317		*<p>This function is derived from the International Astronomical Union's
1318		* SOFA (Standards Of Fundamental Astronomy) software collection.
1319		*
1320		*<p>Status: support function.
1321		*
1322		*<!-- Given: -->
1323		* @param tta double TT as a 2-part Julian Date (Note 1)
1324		* @param ttb double TT as a 2-part Julian Date (Note 1)
1325		* @param uta double UT1 as a 2-part Julian Date (Note 1)
1326		* @param utb double UT1 as a 2-part Julian Date (Note 1)
1327		* @param xp double coordinates of the pole (radians, Note 2)
1328		* @param yp double coordinates of the pole (radians, Note 2)
1329		*
1330		*<!-- Returned: -->
1331		* @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 3)
1332		*
1333		* <p>Notes:
1334		* <ol>
1335		*
1336		* <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1337		* apportioned in any convenient way between the arguments uta and
1338		* utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1339		* these ways, among others:
1340		*<pre>
1341		* uta utb
1342		*
1343		* 2450123.7 0.0 (JD method)
1344		* 2451545.0 -1421.3 (J2000 method)
1345		* 2400000.5 50123.2 (MJD method)
1346		* 2450123.5 0.2 (date &time method)
1347		*</pre>
1348		* The JD method is the most natural and convenient to use in
1349		* cases where the loss of several decimal digits of resolution is
1350		* acceptable. The J2000 and MJD methods are good compromises
1351		* between resolution and convenience. In the case of uta,utb, the
1352		* date &time method is best matched to the Earth rotation angle
1353		* algorithm used: maximum precision is delivered when the uta
1354		* argument is for 0hrs UT1 on the day in question and the utb
1355		* argument lies in the range 0 to 1, or vice versa.
1356		*
1357		* <li> The arguments xp and yp are the coordinates (in radians) of the
1358		* Celestial Intermediate Pole with respect to the International
1359		* Terrestrial Reference System (see IERS Conventions 2003),
1360		* measured along the meridians to 0 and 90 deg west respectively.
1361		*
1362		* <li> The matrix rc2t transforms from celestial to terrestrial
1363		* coordinates:
1364		*
1365		* [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1366		*
1367		* = rc2t * [CRS]
1368		*
1369		* where [CRS] is a vector in the Geocentric Celestial Reference
1370		* System and [TRS] is a vector in the International Terrestrial
1371		* Reference System (see IERS Conventions 2003), RC2I is the
1372		* celestial-to-intermediate matrix, ERA is the Earth rotation
1373		* angle and RPOM is the polar motion matrix.
1374		*
1375		* <li> A faster, but slightly less accurate result (about 1 mas), can
1376		* be obtained by using instead the jauC2t00b function.
1377		*</ol>
1378		*<p>Called:<ul>
1379		* <li>{@link #jauC2i00a} celestial-to-intermediate matrix, IAU 2000A
1380		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1381		* <li>{@link #jauSp00} the TIO locator s', IERS 2000
1382		* <li>{@link #jauPom00} polar motion matrix
1383		* <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1384		* </ul>
1385		*<p>Reference:
1386		*
1387		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1388		* IERS Technical Note No. 32, BKG (2004)
1389		*
1390		*@version 2009 April 1
1391		*
1392		* @since Release 20101201
1393		*
1394		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1395		*/
1396		public static double[][] jauC2t00a(final double tta, final double ttb, final double uta, final double utb,
1397		final double xp, final double yp)
1398		{
1399	2	double rc2i[][]= new double[3][3], era, sp, rpom[][];
1400
1401
1402		/* Form the celestial-to-intermediate matrix for this TT (IAU 2000A). */
1403	2	rc2i = jauC2i00a(tta, ttb);
1404
1405		/* Predict the Earth rotation angle for this UT1. */
1406	2	era = jauEra00(uta, utb);
1407
1408		/* Estimate s'. */
1409	2	sp = jauSp00(tta, ttb);
1410
1411		/* Form the polar motion matrix. */
1412	2	rpom = jauPom00(xp, yp, sp );
1413
1414		/* Combine to form the celestial-to-terrestrial matrix. */
1415	2	double[][] rc2t = jauC2tcio(rc2i, era, rpom );
1416
1417	2	return rc2t;
1418
1419		}
1420
1421
1422		/**
1423		* Form the celestial to terrestrial matrix given the date, the UT1 and
1424		* the polar motion, using the IAU 2000B nutation model.
1425		*
1426		*<p>This function is derived from the International Astronomical Union's
1427		* SOFA (Standards Of Fundamental Astronomy) software collection.
1428		*
1429		*<p>Status: support function.
1430		*
1431		*<!-- Given: -->
1432		* @param tta double TT as a 2-part Julian Date (Note 1)
1433		* @param ttb double TT as a 2-part Julian Date (Note 1)
1434		* @param uta double UT1 as a 2-part Julian Date (Note 1)
1435		* @param utb double UT1 as a 2-part Julian Date (Note 1)
1436		* @param xp double coordinates of the pole (radians, Note 2)
1437		* @param yp double coordinates of the pole (radians, Note 2)
1438		*
1439		*<!-- Returned: -->
1440		* @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 3)
1441		*
1442		* <p>Notes:
1443		* <ol>
1444		*
1445		* <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1446		* apportioned in any convenient way between the arguments uta and
1447		* utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1448		* these ways, among others:
1449		*<pre>
1450		* uta utb
1451		*
1452		* 2450123.7 0.0 (JD method)
1453		* 2451545.0 -1421.3 (J2000 method)
1454		* 2400000.5 50123.2 (MJD method)
1455		* 2450123.5 0.2 (date &time method)
1456		*</pre>
1457		* The JD method is the most natural and convenient to use in
1458		* cases where the loss of several decimal digits of resolution is
1459		* acceptable. The J2000 and MJD methods are good compromises
1460		* between resolution and convenience. In the case of uta,utb, the
1461		* date &time method is best matched to the Earth rotation angle
1462		* algorithm used: maximum precision is delivered when the uta
1463		* argument is for 0hrs UT1 on the day in question and the utb
1464		* argument lies in the range 0 to 1, or vice versa.
1465		*
1466		* <li> The arguments xp and yp are the coordinates (in radians) of the
1467		* Celestial Intermediate Pole with respect to the International
1468		* Terrestrial Reference System (see IERS Conventions 2003),
1469		* measured along the meridians to 0 and 90 deg west respectively.
1470		*
1471		* <li> The matrix rc2t transforms from celestial to terrestrial
1472		* coordinates:
1473		*
1474		* [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1475		*
1476		* = rc2t * [CRS]
1477		*
1478		* where [CRS] is a vector in the Geocentric Celestial Reference
1479		* System and [TRS] is a vector in the International Terrestrial
1480		* Reference System (see IERS Conventions 2003), RC2I is the
1481		* celestial-to-intermediate matrix, ERA is the Earth rotation
1482		* angle and RPOM is the polar motion matrix.
1483		*
1484		* <li> The present function is faster, but slightly less accurate (about
1485		* 1 mas), than the jauC2t00a function.
1486		*</ol>
1487		*<p>Called:<ul>
1488		* <li>{@link #jauC2i00b} celestial-to-intermediate matrix, IAU 2000B
1489		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1490		* <li>{@link #jauPom00} polar motion matrix
1491		* <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1492		* </ul>
1493		*<p>Reference:
1494		*
1495		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1496		* IERS Technical Note No. 32, BKG (2004)
1497		*
1498		*@version 2009 April 1
1499		*
1500		* @since Release 20101201
1501		*
1502		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1503		*/
1504		public static double[][] jauC2t00b(final double tta, final double ttb, final double uta, final double utb,
1505		final double xp, final double yp )
1506		{
1507		double rc2i[][], era, rpom[][];
1508		double rc2t[][];
1509
1510		/* Form the celestial-to-intermediate matrix for this TT (IAU 2000B). */
1511	2	rc2i =jauC2i00b(tta, ttb);
1512
1513		/* Predict the Earth rotation angle for this UT1. */
1514	2	era = jauEra00(uta, utb);
1515
1516		/* Form the polar motion matrix (neglecting s'). */
1517	2	rpom = jauPom00(xp, yp, 0.0 );
1518
1519		/* Combine to form the celestial-to-terrestrial matrix. */
1520	2	rc2t = jauC2tcio(rc2i, era, rpom );
1521
1522	2	return rc2t;
1523
1524		}
1525
1526
1527		/**
1528		* Form the celestial to terrestrial matrix given the date, the UT1 and
1529		* the polar motion, using the IAU 2006 precession and IAU 2000A
1530		* nutation models.
1531		*
1532		*<p>This function is derived from the International Astronomical Union's
1533		* SOFA (Standards Of Fundamental Astronomy) software collection.
1534		*
1535		*<p>Status: support function.
1536		*
1537		*<!-- Given: -->
1538		* @param tta double TT as a 2-part Julian Date (Note 1)
1539		* @param ttb double TT as a 2-part Julian Date (Note 1)
1540		* @param uta double UT1 as a 2-part Julian Date (Note 1)
1541		* @param utb double UT1 as a 2-part Julian Date (Note 1)
1542		* @param xp double coordinates of the pole (radians, Note 2)
1543		* @param yp double coordinates of the pole (radians, Note 2)
1544		*
1545		*<!-- Returned: -->
1546		* @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 3)
1547		*
1548		* <p>Notes:
1549		* <ol>
1550		*
1551		* <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1552		* apportioned in any convenient way between the arguments uta and
1553		* utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1554		* these ways, among others:
1555		*<pre>
1556		* uta utb
1557		*
1558		* 2450123.7 0.0 (JD method)
1559		* 2451545.0 -1421.3 (J2000 method)
1560		* 2400000.5 50123.2 (MJD method)
1561		* 2450123.5 0.2 (date &time method)
1562		*</pre>
1563		* The JD method is the most natural and convenient to use in
1564		* cases where the loss of several decimal digits of resolution is
1565		* acceptable. The J2000 and MJD methods are good compromises
1566		* between resolution and convenience. In the case of uta,utb, the
1567		* date &time method is best matched to the Earth rotation angle
1568		* algorithm used: maximum precision is delivered when the uta
1569		* argument is for 0hrs UT1 on the day in question and the utb
1570		* argument lies in the range 0 to 1, or vice versa.
1571		*
1572		* <li> The arguments xp and yp are the coordinates (in radians) of the
1573		* Celestial Intermediate Pole with respect to the International
1574		* Terrestrial Reference System (see IERS Conventions 2003),
1575		* measured along the meridians to 0 and 90 deg west respectively.
1576		*
1577		* <li> The matrix rc2t transforms from celestial to terrestrial
1578		* coordinates:
1579		*
1580		* [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1581		*
1582		* = rc2t * [CRS]
1583		*
1584		* where [CRS] is a vector in the Geocentric Celestial Reference
1585		* System and [TRS] is a vector in the International Terrestrial
1586		* Reference System (see IERS Conventions 2003), RC2I is the
1587		* celestial-to-intermediate matrix, ERA is the Earth rotation
1588		* angle and RPOM is the polar motion matrix.
1589		*</ol>
1590		*<p>Called:<ul>
1591		* <li>{@link #jauC2i06a} celestial-to-intermediate matrix, IAU 2006/2000A
1592		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1593		* <li>{@link #jauSp00} the TIO locator s', IERS 2000
1594		* <li>{@link #jauPom00} polar motion matrix
1595		* <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1596		* </ul>
1597		*<p>Reference:
1598		*
1599		* <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
1600		* IERS Technical Note No. 32, BKG
1601		*
1602		*@version 2009 April 1
1603		*
1604		* @since Release 20101201
1605		*
1606		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1607		*/
1608		public static double[][] jauC2t06a(final double tta, final double ttb, final double uta, final double utb,
1609		final double xp, final double yp)
1610		{
1611		double rc2i[][], era, sp, rpom[][], rc2t[][];
1612
1613
1614		/* Form the celestial-to-intermediate matrix for this TT. */
1615	2	rc2i = jauC2i06a(tta, ttb);
1616
1617		/* Predict the Earth rotation angle for this UT1. */
1618	2	era = jauEra00(uta, utb);
1619
1620		/* Estimate s'. */
1621	2	sp = jauSp00(tta, ttb);
1622
1623		/* Form the polar motion matrix. */
1624	2	rpom = jauPom00(xp, yp, sp );
1625
1626		/* Combine to form the celestial-to-terrestrial matrix. */
1627	2	rc2t = jauC2tcio(rc2i, era, rpom );
1628
1629	2	return rc2t;
1630
1631		}
1632
1633
1634		/**
1635		* Assemble the celestial to terrestrial matrix from CIO-based
1636		* components (the celestial-to-intermediate matrix, the Earth Rotation
1637		* Angle and the polar motion matrix).
1638		*
1639		*<p>This function is derived from the International Astronomical Union's
1640		* SOFA (Standards Of Fundamental Astronomy) software collection.
1641		*
1642		*<p>Status: support function.
1643		*
1644		*<!-- Given: -->
1645		* @param rc2i double[3][3] celestial-to-intermediate matrix
1646		* @param era double Earth rotation angle (radians)
1647		* @param rpom double[3][3] polar-motion matrix
1648		*
1649		*<!-- Returned: -->
1650		* @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix
1651		*
1652		* <p>Notes:
1653		* <ol>
1654		*
1655		* <li> This function constructs the rotation matrix that transforms
1656		* vectors in the celestial system into vectors in the terrestrial
1657		* system. It does so starting from precomputed components, namely
1658		* the matrix which rotates from celestial coordinates to the
1659		* intermediate frame, the Earth rotation angle and the polar motion
1660		* matrix. One use of the present function is when generating a
1661		* series of celestial-to-terrestrial matrices where only the Earth
1662		* Rotation Angle changes, avoiding the considerable overhead of
1663		* recomputing the precession-nutation more often than necessary to
1664		* achieve given accuracy objectives.
1665		*
1666		* <li> The relationship between the arguments is as follows:
1667		*
1668		* [TRS] = RPOM * R_3(ERA) * rc2i * [CRS]
1669		*
1670		* = rc2t * [CRS]
1671		*
1672		* where [CRS] is a vector in the Geocentric Celestial Reference
1673		* System and [TRS] is a vector in the International Terrestrial
1674		* Reference System (see IERS Conventions 2003).
1675		*</ol>
1676		*<p>Called:<ul>
1677		* <li>{@link #jauCr} copy r-matrix
1678		* <li>{@link #jauRz} rotate around Z-axis
1679		* <li>{@link #jauRxr} product of two r-matrices
1680		* </ul>
1681		*<p>Reference:
1682		*
1683		* <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
1684		* IERS Technical Note No. 32, BKG
1685		*
1686		*@version 2008 May 11
1687		*
1688		* @since Release 20101201
1689		*
1690		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1691		*/
1692		public static double[][] jauC2tcio(final double rc2i[][], final double era, final double rpom[][])
1693		{
1694	10	double r[][] = new double[3][3];
1695
1696
1697		/* Construct the matrix. */
1698	10	jauCr(rc2i, r);
1699	10	jauRz(era, r);
1700	10	double[][] rc2t = jauRxr(rpom, r);
1701
1702	10	return rc2t;
1703
1704		}
1705
1706
1707		/**
1708		* Assemble the celestial to terrestrial matrix from equinox-based
1709		* components (the celestial-to-true matrix, the Greenwich Apparent
1710		* Sidereal Time and the polar motion matrix).
1711		*
1712		*<p>This function is derived from the International Astronomical Union's
1713		* SOFA (Standards Of Fundamental Astronomy) software collection.
1714		*
1715		*<p>Status: support function.
1716		*
1717		*<!-- Given: -->
1718		* @param rbpn double[3][3] celestial-to-true matrix
1719		* @param gst double Greenwich (apparent) Sidereal Time (radians)
1720		* @param rpom double[3][3] polar-motion matrix
1721		*
1722		*<!-- Returned: -->
1723		* @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 2)
1724		*
1725		* <p>Notes:
1726		* <ol>
1727		*
1728		* <li> This function constructs the rotation matrix that transforms
1729		* vectors in the celestial system into vectors in the terrestrial
1730		* system. It does so starting from precomputed components, namely
1731		* the matrix which rotates from celestial coordinates to the
1732		* true equator and equinox of date, the Greenwich Apparent Sidereal
1733		* Time and the polar motion matrix. One use of the present function
1734		* is when generating a series of celestial-to-terrestrial matrices
1735		* where only the Sidereal Time changes, avoiding the considerable
1736		* overhead of recomputing the precession-nutation more often than
1737		* necessary to achieve given accuracy objectives.
1738		*
1739		* <li> The relationship between the arguments is as follows:
1740		*
1741		* [TRS] = rpom * R_3(gst) * rbpn * [CRS]
1742		*
1743		* = rc2t * [CRS]
1744		*
1745		* where [CRS] is a vector in the Geocentric Celestial Reference
1746		* System and [TRS] is a vector in the International Terrestrial
1747		* Reference System (see IERS Conventions 2003).
1748		*</ol>
1749		*<p>Called:<ul>
1750		* <li>{@link #jauCr} copy r-matrix
1751		* <li>{@link #jauRz} rotate around Z-axis
1752		* <li>{@link #jauRxr} product of two r-matrices
1753		* </ul>
1754		*<p>Reference:
1755		*
1756		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1757		* IERS Technical Note No. 32, BKG (2004)
1758		*
1759		*@version 2008 May 11
1760		*
1761		* @since Release 20101201
1762		*
1763		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1764		*/
1765		public static double[][] jauC2teqx(final double rbpn[][], final double gst, final double rpom[][] )
1766		{
1767	4	double r[][] = new double[3][3], rc2t[][];
1768
1769
1770		/* Construct the matrix. */
1771	4	jauCr(rbpn, r);
1772	4	jauRz(gst, r);
1773	4	rc2t = jauRxr(rpom, r);
1774
1775	4	return rc2t;
1776
1777		}
1778
1779
1780		/**
1781		* Form the celestial to terrestrial matrix given the date, the UT1,
1782		* the nutation and the polar motion. IAU 2000.
1783		*
1784		*<p>This function is derived from the International Astronomical Union's
1785		* SOFA (Standards Of Fundamental Astronomy) software collection.
1786		*
1787		*<p>Status: support function.
1788		*
1789		*<!-- Given: -->
1790		* @param tta double TT as a 2-part Julian Date (Note 1)
1791		* @param ttb double TT as a 2-part Julian Date (Note 1)
1792		* @param uta double UT1 as a 2-part Julian Date (Note 1)
1793		* @param utb double UT1 as a 2-part Julian Date (Note 1)
1794		* @param dpsi double nutation (Note 2)
1795		* @param deps double nutation (Note 2)
1796		* @param xp double coordinates of the pole (radians, Note 3)
1797		* @param yp double coordinates of the pole (radians, Note 3)
1798		*
1799		*<!-- Returned: -->
1800		* @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 4)
1801		*
1802		* <p>Notes:
1803		* <ol>
1804		*
1805		* <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1806		* apportioned in any convenient way between the arguments uta and
1807		* utb. For example, JD(UT1)=2450123.7 could be expressed in any of
1808		* these ways, among others:
1809		*<pre>
1810		* uta utb
1811		*
1812		* 2450123.7 0.0 (JD method)
1813		* 2451545.0 -1421.3 (J2000 method)
1814		* 2400000.5 50123.2 (MJD method)
1815		* 2450123.5 0.2 (date &time method)
1816		*</pre>
1817		* The JD method is the most natural and convenient to use in
1818		* cases where the loss of several decimal digits of resolution is
1819		* acceptable. The J2000 and MJD methods are good compromises
1820		* between resolution and convenience. In the case of uta,utb, the
1821		* date &time method is best matched to the Earth rotation angle
1822		* algorithm used: maximum precision is delivered when the uta
1823		* argument is for 0hrs UT1 on the day in question and the utb
1824		* argument lies in the range 0 to 1, or vice versa.
1825		*
1826		* <li> The caller is responsible for providing the nutation components;
1827		* they are in longitude and obliquity, in radians and are with
1828		* respect to the equinox and ecliptic of date. For high-accuracy
1829		* applications, free core nutation should be included as well as
1830		* any other relevant corrections to the position of the CIP.
1831		*
1832		* <li> The arguments xp and yp are the coordinates (in radians) of the
1833		* Celestial Intermediate Pole with respect to the International
1834		* Terrestrial Reference System (see IERS Conventions 2003),
1835		* measured along the meridians to 0 and 90 deg west respectively.
1836		*
1837		* <li> The matrix rc2t transforms from celestial to terrestrial
1838		* coordinates:
1839		*
1840		* [TRS] = RPOM * R_3(GST) * RBPN * [CRS]
1841		*
1842		* = rc2t * [CRS]
1843		*
1844		* where [CRS] is a vector in the Geocentric Celestial Reference
1845		* System and [TRS] is a vector in the International Terrestrial
1846		* Reference System (see IERS Conventions 2003), RBPN is the
1847		* bias-precession-nutation matrix, GST is the Greenwich (apparent)
1848		* Sidereal Time and RPOM is the polar motion matrix.
1849		*
1850		* <li> Although its name does not include "00", This function is in fact
1851		* specific to the IAU 2000 models.
1852		*</ol>
1853		*<p>Called:<ul>
1854		* <li>{@link #jauPn00} bias/precession/nutation results, IAU 2000
1855		* <li>{@link #jauGmst00} Greenwich mean sidereal time, IAU 2000
1856		* <li>{@link #jauSp00} the TIO locator s', IERS 2000
1857		* <li>{@link #jauEe00} equation of the equinoxes, IAU 2000
1858		* <li>{@link #jauPom00} polar motion matrix
1859		* <li>{@link #jauC2teqx} form equinox-based celestial-to-terrestrial matrix
1860		* </ul>
1861		*<p>Reference:
1862		*
1863		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1864		* IERS Technical Note No. 32, BKG (2004)
1865		*
1866		*@version 2009 April 1
1867		*
1868		* @since Release 20101201
1869		*
1870		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1871		*/
1872		public static double[][] jauC2tpe(final double tta, final double ttb, final double uta, final double utb,
1873		final double dpsi, final double deps, final double xp, final double yp)
1874		{
1875		double rpom[][];
1876
1877		/* Form the celestial-to-true matrix for this TT. */
1878	2	PrecessionNutation pn = jauPn00(tta, ttb, dpsi, deps);
1879
1880		/* Predict the Greenwich Mean Sidereal Time for this UT1 and TT. */
1881	2	double gmst = jauGmst00(uta, utb, tta, ttb);
1882
1883		/* Predict the equation of the equinoxes given TT and nutation. */
1884	2	double ee = jauEe00(tta, ttb, pn.epsa, dpsi);
1885
1886		/* Estimate s'. */
1887	2	double sp = jauSp00(tta, ttb);
1888
1889		/* Form the polar motion matrix. */
1890	2	rpom = jauPom00(xp, yp, sp);
1891
1892		/* Combine to form the celestial-to-terrestrial matrix. */
1893	2	double[][] rc2t = jauC2teqx(pn.rbpn, gmst + ee, rpom );
1894
1895	2	return rc2t;
1896
1897		}
1898
1899
1900		/**
1901		* Form the celestial to terrestrial matrix given the date, the UT1,
1902		* the CIP coordinates and the polar motion. IAU 2000.
1903		*
1904		*<p>This function is derived from the International Astronomical Union's
1905		* SOFA (Standards Of Fundamental Astronomy) software collection.
1906		*
1907		*<p>Status: support function.
1908		*
1909		*<!-- Given: -->
1910		* @param tta double TT as a 2-part Julian Date (Note 1)
1911		* @param ttb double TT as a 2-part Julian Date (Note 1)
1912		* @param uta double UT1 as a 2-part Julian Date (Note 1)
1913		* @param utb double UT1 as a 2-part Julian Date (Note 1)
1914		* @param x double Celestial Intermediate Pole (Note 2)
1915		* @param y double Celestial Intermediate Pole (Note 2)
1916		* @param xp double coordinates of the pole (radians, Note 3)
1917		* @param yp double coordinates of the pole (radians, Note 3)
1918		*
1919		*<!-- Returned: -->
1920		* @return rc2t double[3][3] <u>returned</u> celestial-to-terrestrial matrix (Note 4)
1921		*
1922		* <p>Notes:
1923		* <ol>
1924		*
1925		* <li> The TT and UT1 dates tta+ttb and uta+utb are Julian Dates,
1926		* apportioned in any convenient way between the arguments uta and
1927		* utb. For example, JD(UT1)=2450123.7 could be expressed in any o
1928		* these ways, among others:
1929		*<pre>
1930		* uta utb
1931		*
1932		* 2450123.7 0.0 (JD method)
1933		* 2451545.0 -1421.3 (J2000 method)
1934		* 2400000.5 50123.2 (MJD method)
1935		* 2450123.5 0.2 (date &time method)
1936		*</pre>
1937		* The JD method is the most natural and convenient to use in
1938		* cases where the loss of several decimal digits of resolution is
1939		* acceptable. The J2000 and MJD methods are good compromises
1940		* between resolution and convenience. In the case of uta,utb, the
1941		* date &time method is best matched to the Earth rotation angle
1942		* algorithm used: maximum precision is delivered when the uta
1943		* argument is for 0hrs UT1 on the day in question and the utb
1944		* argument lies in the range 0 to 1, or vice versa.
1945		*
1946		* <li> The Celestial Intermediate Pole coordinates are the x,y
1947		* components of the unit vector in the Geocentric Celestial
1948		* Reference System.
1949		*
1950		* <li> The arguments xp and yp are the coordinates (in radians) of the
1951		* Celestial Intermediate Pole with respect to the International
1952		* Terrestrial Reference System (see IERS Conventions 2003),
1953		* measured along the meridians to 0 and 90 deg west respectively.
1954		*
1955		* <li> The matrix rc2t transforms from celestial to terrestrial
1956		* coordinates:
1957		*
1958		* [TRS] = RPOM * R_3(ERA) * RC2I * [CRS]
1959		*
1960		* = rc2t * [CRS]
1961		*
1962		* where [CRS] is a vector in the Geocentric Celestial Reference
1963		* System and [TRS] is a vector in the International Terrestrial
1964		* Reference System (see IERS Conventions 2003), ERA is the Earth
1965		* Rotation Angle and RPOM is the polar motion matrix.
1966		*
1967		* <li> Although its name does not include "00", This function is in fact
1968		* specific to the IAU 2000 models.
1969		*</ol>
1970		*<p>Called:<ul>
1971		* <li>{@link #jauC2ixy} celestial-to-intermediate matrix, given X,Y
1972		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
1973		* <li>{@link #jauSp00} the TIO locator s', IERS 2000
1974		* <li>{@link #jauPom00} polar motion matrix
1975		* <li>{@link #jauC2tcio} form CIO-based celestial-to-terrestrial matrix
1976		* </ul>
1977		* Reference:
1978		*
1979		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
1980		* IERS Technical Note No. 32, BKG (2004)
1981		*
1982		*@version 2009 April 1
1983		*
1984		* @since Release 20101201
1985		*
1986		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
1987		*/
1988		public static double[][] jauC2txy(double tta, double ttb, double uta, double utb,
1989		double x, double y, double xp, double yp)
1990		{
1991	2	double rc2i[][] = new double[3][3], era, sp, rpom[][] = new double[3][3];
1992
1993
1994		/* Form the celestial-to-intermediate matrix for this TT. */
1995	2	rc2i = jauC2ixy(tta, ttb, x, y);
1996
1997		/* Predict the Earth rotation angle for this UT1. */
1998	2	era = jauEra00(uta, utb);
1999
2000		/* Estimate s'. */
2001	2	sp = jauSp00(tta, ttb);
2002
2003		/* Form the polar motion matrix. */
2004	2	rpom = jauPom00(xp, yp, sp);
2005
2006		/* Combine to form the celestial-to-terrestrial matrix. */
2007	2	double[][] rc2t = jauC2tcio(rc2i, era, rpom );
2008
2009	2	return rc2t;
2010
2011		}
2012
2013		/**
2014		* Gregorian Calendar to Julian Date.
2015		*
2016		*<p>This function is derived from the International Astronomical Union's
2017		* SOFA (Standards Of Fundamental Astronomy) software collection.
2018		*
2019		*<p>Status: support function.
2020		*
2021		*<!-- Given: -->
2022		* @param iy,im,id int year, month, day in Gregorian calendar (Note 1)
2023		*
2024		*<!-- Returned: -->
2025		* @return d MJD zero-point: always 2400000.5
2026		* <u>returned</u> Modified Julian Date for 0 hrs
2027		*
2028		* <!-- Returned (function value): -->
2029		* @throws JSOFAIllegalParameter status:
2030		* 0 = OK
2031		* -1 = bad year (Note 3: JD not computed)
2032		* -2 = bad month (JD not computed)
2033		* -3 = bad day (JD computed)
2034		*
2035		* <p>Notes:
2036		* <ol>
2037		*
2038		* <li> The algorithm used is valid from -4800 March 1, but this
2039		* implementation rejects dates before -4799 January 1.
2040		*
2041		* <li> The Julian Date is returned in two pieces, in the usual JSOFA
2042		* manner, which is designed to preserve time resolution. The
2043		* Julian Date is available as a single number by adding djm0 and
2044		* djm.
2045		*
2046		* <li> In early eras the conversion is from the "Proleptic Gregorian
2047		* Calendar"; no account is taken of the date(s) of adoption of
2048		* the Gregorian Calendar, nor is the AD/BC numbering convention
2049		* observed.
2050		*</ol>
2051		*<p>Reference:
2052		*
2053		* <p>Explanatory Supplement to the Astronomical Almanac,
2054		* P. Kenneth Seidelmann (ed), University Science Books (1992),
2055		* Section 12.92 (p604).
2056		*
2057		*@version 2009 October 19
2058		*
2059		* @since Release 20101201
2060		*
2061		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2062		*/
2063		public static JulianDate jauCal2jd(int iy, int im, int id) throws JSOFAIllegalParameter
2064		{
2065		int ly, my;
2066		long iypmy;
2067		double djm0, djm;
2068
2069		/* Earliest year allowed (4800BC) */
2070	224	final int IYMIN = -4799;
2071
2072		/* Month lengths in days */
2073	224	final int mtab[]
2074		= {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
2075
2076
2077		/* Validate year and month. */
2078	224	if (iy < IYMIN) throw new JSOFAIllegalParameter("bad year", -1);
2079	224	if (im < 1 \|\| im > 12) throw new JSOFAIllegalParameter("bad month", -2);
2080
2081		/* If February in a leap year, 1, otherwise 0. */
2082	224	ly = ((im == 2) &&(iy%4 == 0) && (iy%100 != 0 \|\| (iy%400 == 0)))?1:0;
2083
2084		/* Validate day, taking into account leap years. */
2085	224	if ( (id < 1) \|\| (id > (mtab[im-1] + ly))) {
2086		}
2087
2088		/* Return result. */
2089	224	my = (im - 14) / 12;
2090	224	iypmy = (long) (iy + my);
2091	224	djm0 = DJM0;
2092	224	djm = (double)((1461L * (iypmy + 4800L)) / 4L
2093		+ (367L * (long) (im - 2 - 12 * my)) / 12L
2094		- (3L * ((iypmy + 4900L) / 100L)) / 4L
2095		+ (long) id - 2432076L);
2096
2097		/* Return status. */
2098	224	return new JulianDate(djm0, djm);
2099
2100		}
2101
2102
2103		/**
2104		* Copy a p-vector.
2105		*
2106		*<p>This function is derived from the International Astronomical Union's
2107		* SOFA (Standards Of Fundamental Astronomy) software collection.
2108		*
2109		*<p>Status: vector/matrix support function.
2110		*
2111		*<!-- Given: -->
2112		* @param p double[3] p-vector to be copied
2113		*
2114		*<!-- Returned: -->
2115		* @param c double[3] <u>given and returned</u> copy
2116		*
2117		*@version 2008 May 11
2118		*
2119		* @since Release 20101201
2120		*
2121		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2122		*/
2123		public static double[] jauCp(double p[], double c[])
2124		{
2125
2126	3616	c[0] = p[0];
2127	3616	c[1] = p[1];
2128	3616	c[2] = p[2];
2129
2130	3616	return c;
2131
2132		}
2133
2134
2135		/**
2136		* Copy a position/velocity vector.
2137		*
2138		*<p>This function is derived from the International Astronomical Union's
2139		* SOFA (Standards Of Fundamental Astronomy) software collection.
2140		*
2141		*<p>Status: vector/matrix support function.
2142		*
2143		*<!-- Given: -->
2144		* @param pv double[2][3] position/velocity vector to be copied
2145		*
2146		*<!-- Returned: -->
2147		* @return c double[2][3] <u>returned</u> copy
2148		*
2149		*<p>Called:<ul>
2150		* <li>{@link #jauCp} copy p-vector
2151		* </ul>
2152		*@version 2008 May 11
2153		*
2154		* @since Release 20101201
2155		*
2156		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2157		*/
2158		public static double[][] jauCpv(double pv[][], double c[][])
2159		{
2160
2161	16	c[0]=jauCp(pv[0], c[0]);
2162	16	c[1]=jauCp(pv[1], c[1]);
2163
2164	16	return c;
2165
2166		}
2167
2168
2169		/**
2170		* Copy an r-matrix.
2171		*
2172		*<p>This function is derived from the International Astronomical Union's
2173		* SOFA (Standards Of Fundamental Astronomy) software collection.
2174		*
2175		*<p>Status: vector/matrix support function.
2176		*
2177		*<!-- Given: -->
2178		* @param r double[3][3] r-matrix to be copied.
2179		*
2180		*<!-- Returned: -->
2181		* @param c double[3][3] <u>given and returned</u> the elements of r are copied into this.
2182		*
2183		*<p>Called:<ul>
2184		* <li>{@link #jauCp} copy p-vector
2185		* </ul>
2186		*@version 2008 May 11
2187		*
2188		* @since Release 20101201
2189		*
2190		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2191		*/
2192		public static void jauCr(double r[][], double c[][] )
2193		{
2194
2195	1172	jauCp(r[0], c[0]);
2196	1172	jauCp(r[1], c[1]);
2197	1172	jauCp(r[2], c[2]);
2198
2199	1172	return;
2200
2201		}
2202
2203
2204		/**
2205		* Decompose days to hours, minutes, seconds, fraction.
2206		*
2207		*<p>This function is derived from the International Astronomical Union's
2208		* SOFA (Standards Of Fundamental Astronomy) software collection.
2209		*
2210		*<p>Status: vector/matrix support function.
2211		*
2212		*<!-- Given: -->
2213		* @param ndp int resolution (Note 1)
2214		* @param days double interval in days
2215		*
2216		*<!-- Returned: -->
2217		* @param ihmsf int[4] <u>returned</u> hours, minutes, seconds, fraction
2218		* @return sign char <u>returned</u> '+' or '-'
2219		*
2220		* <p>Notes:
2221		* <ol>
2222		*
2223		* <li> The argument ndp is interpreted as follows:
2224		*
2225		* ndp resolution
2226		* : ...0000 00 00
2227		* -7 1000 00 00
2228		* -6 100 00 00
2229		* -5 10 00 00
2230		* -4 1 00 00
2231		* -3 0 10 00
2232		* -2 0 01 00
2233		* -1 0 00 10
2234		* 0 0 00 01
2235		* 1 0 00 00.1
2236		* 2 0 00 00.01
2237		* 3 0 00 00.001
2238		* : 0 00 00.000...
2239		*
2240		* <li> The largest positive useful value for ndp is determined by the
2241		* size of days, the format of double on the target platform, and
2242		* the risk of overflowing ihmsf[3]. On a typical platform, for
2243		* days up to 1.0, the available floating-point precision might
2244		* correspond to ndp=12. However, the practical limit is typically
2245		* ndp=9, set by the capacity of a 32-bit int, or ndp=4 if int is
2246		* only 16 bits.
2247		*
2248		* <li> The absolute value of days may exceed 1.0. In cases where it
2249		* does not, it is up to the caller to test for and handle the
2250		* case where days is very nearly 1.0 and rounds up to 24 hours,
2251		* by testing for ihms[0]=24 and setting ihmsf[0-3] to zero.
2252		*</ol>
2253		*@version 2008 May 11
2254		*
2255		* @since Release 20101201
2256		*
2257		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2258		*/
2259		public static char jauD2tf(final int ndp, final double days, int ihmsf[])
2260		{
2261		int nrs, n;
2262		double rs, rm, rh, a, w, ah, am, as, af;
2263
2264
2265		/* Handle sign. */
2266	8	char sign = (char) ( ( days >= 0.0 ) ? '+' : '-' );
2267
2268		/* Interval in seconds. */
2269	8	a = DAYSEC * abs(days);
2270
2271		/* Pre-round if resolution coarser than 1s (then pretend ndp=1). */
2272	8	if (ndp < 0) {
2273	0	nrs = 1;
2274	0	for (n = 1; n <= -ndp; n++) {
2275	0	nrs *= (n == 2 \|\| n == 4) ? 6 : 10;
2276		}
2277	0	rs = (double) nrs;
2278	0	w = a / rs;
2279	0	a = rs * dnint(w);
2280		}
2281
2282		/* Express the unit of each field in resolution units. */
2283	8	nrs = 1;
2284	42	for (n = 1; n <= ndp; n++) {
2285	34	nrs *= 10;
2286		}
2287	8	rs = (double) nrs;
2288	8	rm = rs * 60.0;
2289	8	rh = rm * 60.0;
2290
2291		/* Round the interval and express in resolution units. */
2292	8	a = dnint(rs * a);
2293
2294		/* Break into fields. */
2295	8	ah = a / rh;
2296	8	ah = dint(ah);
2297	8	a -= ah * rh;
2298	8	am = a / rm;
2299	8	am = dint(am);
2300	8	a -= am * rm;
2301	8	as = a / rs;
2302	8	as = dint(as);
2303	8	af = a - as * rs;
2304
2305		/* Return results. */
2306	8	ihmsf[0] = (int) ah;
2307	8	ihmsf[1] = (int) am;
2308	8	ihmsf[2] = (int) as;
2309	8	ihmsf[3] = (int) af;
2310
2311	8	return sign;
2312
2313		}
2314
2315		/**
2316		* Representation of Gregorian Calendar with fractional day.
2317		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
2318		*
2319		* @since AIDA Stage 1
2320		*/
2321		public static class Calendar {
2322		public final int iy;
2323		public final int im;
2324		public final int id;
2325		public final double fd;
2326		public Calendar (int iy, int im, int id, double fd)
2327	162	{
2328	162	this.iy = iy;
2329	162	this.im = im;
2330	162	this.id = id;
2331	162	this.fd = fd;
2332	162	}
2333		}
2334
2335		/**
2336		* Representation of Gregorian Calendar with integer hours minutes and seconds.
2337		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
2338		*
2339		* @since AIDA Stage 1
2340		*/
2341		public static class CalendarHMS {
2342		public final int iy;
2343		public final int im;
2344		public final int id;
2345		public final int ihmsf[];
2346	2	public CalendarHMS (int iy, int im, int id, int hmsf[]){
2347	2	this.iy = iy;
2348	2	this.im = im;
2349	2	this.id = id;
2350	2	this.ihmsf = hmsf;
2351	2	}
2352		}
2353
2354		/**
2355		**
2356		** Format for output a 2-part Julian Date (or in the case of UTC a
2357		** quasi-JD form that includes special provision for leap seconds).
2358		**
2359		**<p>This function is derived from the International Astronomical Union's
2360		** SOFA (Standards of Fundamental Astronomy) software collection.
2361		**
2362		**<p>Status: support function.
2363		**
2364		**<!-- Given: -->
2365		** scale char[] time scale ID (Note 1)
2366		** ndp int resolution (Note 2)
2367		** d1,d2 double time as a 2-part Julian Date (Notes 3,4)
2368		**
2369		**<!-- Returned:-->
2370		** iy,im,id int year, month, day in Gregorian calendar (Note 5)
2371		** ihmsf int[4] hours, minutes, seconds, fraction (Note 1)
2372		**
2373		** Returned (function value):
2374		** int status: +1 = dubious year (Note 5)
2375		** 0 = OK
2376		** -1 = unacceptable date (Note 6)
2377		**
2378		**<p>Notes:
2379		**
2380		** 1) scale identifies the time scale. Only the value "UTC" (in upper
2381		** case) is significant, and enables handling of leap seconds (see
2382		** Note 4).
2383		**
2384		** 2) ndp is the number of decimal places in the seconds field, and can
2385		** have negative as well as positive values, such as:
2386		**
2387		** ndp resolution
2388		** -4 1 00 00
2389		** -3 0 10 00
2390		** -2 0 01 00
2391		** -1 0 00 10
2392		** 0 0 00 01
2393		** 1 0 00 00.1
2394		** 2 0 00 00.01
2395		** 3 0 00 00.001
2396		**
2397		** The limits are platform dependent, but a safe range is -5 to +9.
2398		**
2399		** 3) d1+d2 is Julian Date, apportioned in any convenient way between
2400		** the two arguments, for example where d1 is the Julian Day Number
2401		** and d2 is the fraction of a day. In the case of UTC, where the
2402		** use of JD is problematical, special conventions apply: see the
2403		** next note.
2404		**
2405		** 4) JD cannot unambiguously represent UTC during a leap second unless
2406		** special measures are taken. The SOFA internal convention is that
2407		** the quasi-JD day represents UTC days whether the length is 86399,
2408		** 86400 or 86401 SI seconds. In the 1960-1972 era there were
2409		** smaller jumps (in either direction) each time the linear UTC(TAI)
2410		** expression was changed, and these "mini-leaps" are also included
2411		** in the SOFA convention.
2412		**
2413		** 5) The warning status "dubious year" flags UTCs that predate the
2414		** introduction of the time scale or that are too far in the future
2415		** to be trusted. See iauDat for further details.
2416		**
2417		** 6) For calendar conventions and limitations, see iauCal2jd.
2418		**
2419		** Called:
2420		** iauJd2cal JD to Gregorian calendar
2421		** iauD2tf decompose days to hms
2422		** iauDat delta(AT) = TAI-UTC
2423		**
2424		**@version 2014 February 15
2425		**
2426		**@since JSOFA release 20131202
2427		**
2428		** <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
2429		* @throws JSOFAInternalError
2430		* @throws JSOFAIllegalParameter
2431		*/
2432		public static CalendarHMS jauD2dtf(final String scale, int ndp, double d1, double d2 ) throws JSOFAIllegalParameter, JSOFAInternalError
2433		{
2434		boolean leap;
2435	2	int iy1, im1, id1, iy2, im2, id2, ihmsf1[] = new int[4];
2436		double a1, b1, fd, dat0, dat12, dat24, dleap;
2437
2438
2439		/* The two-part JD. */
2440	2	a1 = d1;
2441	2	b1 = d2;
2442
2443		/* Provisional calendar date. */
2444	2	Calendar cal = jauJd2cal(a1, b1);
2445	2	iy1 = cal.iy;
2446	2	im1 = cal.im;
2447	2	id1 = cal.id;
2448	2	fd = cal.fd;
2449
2450		/* Is this a leap second day? */
2451	2	leap = false;
2452	2	if ( scale.equalsIgnoreCase("UTC") ) {
2453
2454		/* TAI-UTC at 0h today. */
2455	2	dat0 = jauDat(iy1, im1, id1, 0.0 );
2456
2457		/* TAI-UTC at 12h today (to detect drift). */
2458	2	dat12 = jauDat(iy1, im1, id1, 0.5);
2459
2460		/* TAI-UTC at 0h tomorrow (to detect jumps). */
2461	2	cal = jauJd2cal(a1+1.5, b1-fd);
2462	2	iy2 = cal.iy;
2463	2	im2 = cal.im;
2464	2	id2 = cal.id;
2465	2	dat24 = jauDat(iy2, im2, id2, 0.0);
2466
2467		/* Any sudden change in TAI-UTC (seconds). */
2468	2	dleap = dat24 - (2.0*dat12 - dat0);
2469
2470		/* If leap second day, scale the fraction of a day into SI. */
2471	2	leap = (dleap != 0.0);
2472	2	if (leap) fd += fd * dleap/DAYSEC;
2473		}
2474
2475	2	jauD2tf ( ndp, fd, ihmsf1 );
2476
2477		/* Has the (rounded) time gone past 24h? */
2478	2	if ( ihmsf1[0] > 23 ) {
2479
2480		/* Yes. We probably need tomorrow's calendar date. */
2481	2	cal = jauJd2cal(a1+1.5, b1-fd);
2482	2	iy2 = cal.iy; im2 = cal.im; id2 = cal.id;
2483
2484		/* Is today a leap second day? */
2485	2	if ( ! leap ) {
2486
2487		/* No. Use 0h tomorrow. */
2488	0	iy1 = iy2;
2489	0	im1 = im2;
2490	0	id1 = id2;
2491	0	ihmsf1[0] = 0;
2492	0	ihmsf1[1] = 0;
2493	0	ihmsf1[2] = 0;
2494
2495		} else {
2496
2497		/* Yes. Are we past the leap second itself? */
2498	2	if ( ihmsf1[2] > 0 ) {
2499
2500		/* Yes. Use tomorrow but allow for the leap second. */
2501	0	iy1 = iy2;
2502	0	im1 = im2;
2503	0	id1 = id2;
2504	0	ihmsf1[0] = 0;
2505	0	ihmsf1[1] = 0;
2506	0	ihmsf1[2] = 0;
2507
2508		} else {
2509
2510		/* No. Use 23 59 60... today. */
2511	2	ihmsf1[0] = 23;
2512	2	ihmsf1[1] = 59;
2513	2	ihmsf1[2] = 60;
2514		}
2515
2516		/* If rounding to 10s or coarser always go up to new day. */
2517	2	if ( ndp < 0 && ihmsf1[2] == 60 ) {
2518	0	iy1 = iy2;
2519	0	im1 = im2;
2520	0	id1 = id2;
2521	0	ihmsf1[0] = 0;
2522	0	ihmsf1[1] = 0;
2523	0	ihmsf1[2] = 0;
2524		}
2525		}
2526		}
2527
2528		/* Results. */
2529
2530	2	return new CalendarHMS(iy1, im1, id1, ihmsf1);
2531
2532		}
2533
2534		/**
2535		** Encode date and time fields into 2-part Julian Date (or in the case
2536		** of UTC a quasi-JD form that includes special provision for leap
2537		** seconds).
2538		**
2539		**<p>This function is derived from the International Astronomical Union's
2540		** SOFA (Standards of Fundamental Astronomy) software collection.
2541		**
2542		** Status: support function.
2543		**
2544		** Given:
2545		** @param scale char time scale ID (Note 1)
2546		** @param iy,im,id int year, month, day in Gregorian calendar (Note 2)
2547		** @param ihr,imn int hour, minute
2548		** @param sec double seconds
2549		**
2550		** Returned:
2551		** @return 2-part Julian Date (Notes 3,4)
2552		**
2553		* @throws JSOFAIllegalParameter
2554		* @throws JSOFAInternalError
2555		** {@literal status: +3 = both of next two
2556		** +2 = time is after end of day (Note 5)
2557		** +1 = dubious year (Note 6)
2558		** 0 = OK
2559		** -1 = bad year
2560		** -2 = bad month
2561		** -3 = bad day
2562		** -4 = bad hour
2563		** -5 = bad minute
2564		** -6 = bad second (<0)}
2565		**
2566		**<p>Notes:
2567		**
2568		** 1) scale identifies the time scale. Only the value "UTC" (in upper
2569		** case) is significant, and enables handling of leap seconds (see
2570		** Note 4).
2571		**
2572		** 2) For calendar conventions and limitations, see iauCal2jd.
2573		**
2574		** 3) The sum of the results, d1+d2, is Julian Date, where normally d1
2575		** is the Julian Day Number and d2 is the fraction of a day. In the
2576		** case of UTC, where the use of JD is problematical, special
2577		** conventions apply: see the next note.
2578		**
2579		** 4) JD cannot unambiguously represent UTC during a leap second unless
2580		** special measures are taken. The SOFA internal convention is that
2581		** the quasi-JD day represents UTC days whether the length is 86399,
2582		** 86400 or 86401 SI seconds. In the 1960-1972 era there were
2583		** smaller jumps (in either direction) each time the linear UTC(TAI)
2584		** expression was changed, and these "mini-leaps" are also included
2585		** in the SOFA convention.
2586		**
2587		** 5) The warning status "time is after end of day" usually means that
2588		** the sec argument is greater than 60.0. However, in a day ending
2589		** in a leap second the limit changes to 61.0 (or 59.0 in the case
2590		** of a negative leap second).
2591		**
2592		** 6) The warning status "dubious year" flags UTCs that predate the
2593		** introduction of the time scale or that are too far in the future
2594		** to be trusted. See iauDat for further details.
2595		**
2596		** 7) Only in the case of continuous and regular time scales (TAI, TT,
2597		** TCG, TCB and TDB) is the result d1+d2 a Julian Date, strictly
2598		** speaking. In the other cases (UT1 and UTC) the result must be
2599		** used with circumspection; in particular the difference between
2600		** two such results cannot be interpreted as a precise time
2601		** interval.
2602		**
2603		** Called:
2604		** iauCal2jd Gregorian calendar to JD
2605		** iauDat delta(AT) = TAI-UTC
2606		** iauJd2cal JD to Gregorian calendar
2607		**
2608		**@version 2013 July 26
2609		**
2610		**@since JSOFA release 20131202
2611		**
2612		** <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
2613		*/
2614		public static JulianDate jauDtf2d(final String scale, int iy, int im, int id,
2615		int ihr, int imn, double sec) throws JSOFAIllegalParameter, JSOFAInternalError
2616		{
2617	2	int js = 0, iy2, im2, id2;
2618		double dj, w, day, seclim, dat0, dat12, dat24, dleap, time;
2619
2620
2621		/* Today's Julian Day Number. */
2622	2	JulianDate jd = jauCal2jd(iy, im, id);
2623	2	dj = jd.djm0; w = jd.djm1;
2624	2	dj += w;
2625
2626		/* Day length and final minute length in seconds (provisional). */
2627	2	day = DAYSEC;
2628	2	seclim = 60.0;
2629
2630		/* Deal with the UTC leap second case. */
2631	2	if ( scale.equals("UTC") ) {
2632
2633		/* TAI-UTC at 0h today. */
2634	2	dat0 = jauDat(iy, im, id, 0.0);
2635
2636		/* TAI-UTC at 12h today (to detect drift). */
2637	2	dat12 = jauDat(iy, im, id, 0.5);
2638
2639		/* TAI-UTC at 0h tomorrow (to detect jumps). */
2640	2	Calendar cal = jauJd2cal ( dj, 1.5);
2641	2	iy2 = cal.iy; im2 = cal.im; id2 = cal.id; w = cal.fd;
2642
2643	2	dat24 = jauDat(iy2, im2, id2, 0.0);
2644
2645		/* Any sudden change in TAI-UTC between today and tomorrow. */
2646	2	dleap = dat24 - (2.0*dat12 - dat0);
2647
2648		/* If leap second day, correct the day and final minute lengths. */
2649	2	day += dleap;
2650	2	if ( ihr == 23 && imn == 59 ) seclim += dleap;
2651
2652		/* End of UTC-specific actions. */
2653		}
2654
2655		/* Validate the time. */
2656	2	if ( ihr >= 0 && ihr <= 23 ) {
2657	2	if ( imn >= 0 && imn <= 59 ) {
2658	2	if ( sec >= 0 ) {
2659	2	if ( sec >= seclim ) {
2660	0	js += 2;
2661		}
2662		} else {
2663	0	js = -6;
2664		}
2665		} else {
2666	0	js = -5;
2667		}
2668		} else {
2669	0	js = -4;
2670		}
2671	2	if ( js < 0 ) throw new JSOFAInternalError("problem with time", js);
2672
2673		/* The time in days. */
2674	2	time = ( 60.0 * ( (double) ( 60 * ihr + imn ) ) + sec ) / day;
2675
2676		/* Return the date and time. */
2677	2	return new JulianDate(dj, time) ;
2678
2679		}
2680
2681
2682
2683		/** Release year for this version of jauDat {@value} */
2684		public final static int IYV = 2016;
2685		static class LeapInfo {
2686		final public int iyear, month;
2687		final public double delat;
2688	84	public LeapInfo(int i, int m, double t) {
2689	84	iyear = i;
2690	84	month = m;
2691	84	delat = t;
2692	84	}
2693		}
2694
2695		/* Dates and Delta(AT)s */
2696	2	static final LeapInfo leapSeconds[] = {
2697		new LeapInfo( 1960, 1, 1.4178180 ),
2698		new LeapInfo( 1961, 1, 1.4228180 ),
2699		new LeapInfo( 1961, 8, 1.3728180 ),
2700		new LeapInfo( 1962, 1, 1.8458580 ),
2701		new LeapInfo( 1963, 11, 1.9458580 ),
2702		new LeapInfo( 1964, 1, 3.2401300 ),
2703		new LeapInfo( 1964, 4, 3.3401300 ),
2704		new LeapInfo( 1964, 9, 3.4401300 ),
2705		new LeapInfo( 1965, 1, 3.5401300 ),
2706		new LeapInfo( 1965, 3, 3.6401300 ),
2707		new LeapInfo( 1965, 7, 3.7401300 ),
2708		new LeapInfo( 1965, 9, 3.8401300 ),
2709		new LeapInfo( 1966, 1, 4.3131700 ),
2710		new LeapInfo( 1968, 2, 4.2131700 ),
2711		new LeapInfo( 1972, 1, 10.0 ),
2712		new LeapInfo( 1972, 7, 11.0 ),
2713		new LeapInfo( 1973, 1, 12.0 ),
2714		new LeapInfo( 1974, 1, 13.0 ),
2715		new LeapInfo( 1975, 1, 14.0 ),
2716		new LeapInfo( 1976, 1, 15.0 ),
2717		new LeapInfo( 1977, 1, 16.0 ),
2718		new LeapInfo( 1978, 1, 17.0 ),
2719		new LeapInfo( 1979, 1, 18.0 ),
2720		new LeapInfo( 1980, 1, 19.0 ),
2721		new LeapInfo( 1981, 7, 20.0 ),
2722		new LeapInfo( 1982, 7, 21.0 ),
2723		new LeapInfo( 1983, 7, 22.0 ),
2724		new LeapInfo( 1985, 7, 23.0 ),
2725		new LeapInfo( 1988, 1, 24.0 ),
2726		new LeapInfo( 1990, 1, 25.0 ),
2727		new LeapInfo( 1991, 1, 26.0 ),
2728		new LeapInfo( 1992, 7, 27.0 ),
2729		new LeapInfo( 1993, 7, 28.0 ),
2730		new LeapInfo( 1994, 7, 29.0 ),
2731		new LeapInfo( 1996, 1, 30.0 ),
2732		new LeapInfo( 1997, 7, 31.0 ),
2733		new LeapInfo( 1999, 1, 32.0 ),
2734		new LeapInfo( 2006, 1, 33.0 ),
2735		new LeapInfo( 2009, 1, 34.0 ),
2736		new LeapInfo( 2012, 7, 35.0 ),
2737		new LeapInfo( 2015, 7, 36.0 ),
2738		new LeapInfo( 2017, 1, 37.0 )
2739		};
2740
2741		/**
2742		* For a given UTC date, calculate delta(AT) = TAI-UTC.
2743		*<pre>
2744		* :------------------------------------------:
2745		* : :
2746		* : IMPORTANT :
2747		* : :
2748		* : A new version of this function must be :
2749		* : produced whenever a new leap second is :
2750		* : announced. There are four items to :
2751		* : change on each such occasion: :
2752		* : :
2753		* : 1) A new line must be added to the set :
2754		* : of statements that initialize the :
2755		* : array "changes". :
2756		* : :
2757		* : 2) The parameter IYV must be set to :
2758		* : the current year. :
2759		* : :
2760		* : 3) The "Latest leap second" comment :
2761		* : below must be set to the new leap :
2762		* : second date. :
2763		* : :
2764		* : 4) The "This revision" comment, later, :
2765		* : must be set to the current date. :
2766		* : :
2767		* : Change (2) must also be carried out :
2768		* : whenever the function is re-issued, :
2769		* : even if no leap seconds have been :
2770		* : added. :
2771		* : :
2772		* : Latest leap second: 2017 Jan 01 :
2773		* : :
2774		* :__________________________________________:
2775		*</pre>
2776		*<p>This function is derived from the International Astronomical Union's
2777		* SOFA (Standards Of Fundamental Astronomy) software collection.
2778		*
2779		*<p>Status: support function.
2780		*
2781		*<!-- Given: -->
2782		* @param iy int UTC: year (Notes 1 and 2)
2783		* @param im int month (Note 2)
2784		* @param id int day (Notes 2 and 3)
2785		* @param fd double fraction of day (Note 4)
2786		*
2787		*<!-- Returned: -->
2788		* @return deltat double <u>returned</u> TAI minus UTC, seconds
2789		*
2790		* @throws JSOFAIllegalParameter status (Note 5):
2791		* 1 = dubious year (Note 1)
2792		* 0 = OK
2793		* -1 = bad year
2794		* -2 = bad month
2795		* -3 = bad day (Note 3)
2796		* -4 = bad fraction (Note 4)
2797		*
2798		* <p>Notes:
2799		* <ol>
2800		*
2801		* <li> UTC began at 1960 January 1.0 (JD 2436934.5) and it is improper
2802		* to call the function with an earlier date. If this is attempted,
2803		* zero is returned together with a warning status.
2804		*
2805		* Because leap seconds cannot, in principle, be predicted in
2806		* advance, a reliable check for dates beyond the valid range is
2807		* impossible. To guard against gross errors, a year five or more
2808		* after the release year of the present function (see parameter
2809		* IYV) is considered dubious. In this case a warning status is
2810		* returned but the result is computed in the normal way.
2811		*
2812		* For both too-early and too-late years, the warning status is
2813		* j=+1. This is distinct from the error status j=-1, which
2814		* signifies a year so early that JD could not be computed.
2815		*
2816		* <li> If the specified date is for a day which ends with a leap second,
2817		* the UTC-TAI value returned is for the period leading up to the
2818		* leap second. If the date is for a day which begins as a leap
2819		* second ends, the UTC-TAI returned is for the period following the
2820		* leap second.
2821		*
2822		* <li> The day number must be in the normal calendar range, for example
2823		* 1 through 30 for April. The "almanac" convention of allowing
2824		* such dates as January 0 and December 32 is not supported in this
2825		* function, in order to avoid confusion near leap seconds.
2826		*
2827		* <li> The fraction of day is used only for dates before the
2828		* introduction of leap seconds, the first of which occurred at the
2829		* end of 1971. It is tested for validity (zero to less than 1 is
2830		* the valid range) even if not used; if invalid, zero is used and
2831		* status j=-4 is returned. For many applications, setting fd to
2832		* zero is acceptable; the resulting error is always less than 3 ms
2833		* (and occurs only pre-1972).
2834		*
2835		* <li> The status value returned in the case where there are multiple
2836		* errors refers to the first error detected. For example, if the
2837		* month and day are 13 and 32 respectively, j=-2 (bad month)
2838		* will be returned.
2839		*
2840		* <li> In cases where a valid result is not available, zero is returned.
2841		*
2842		*<p>References:
2843		*
2844		* <li> For dates from 1961 January 1 onwards, the expressions from the
2845		* file ftp://maia.usno.navy.mil/ser7/tai-utc.dat are used.
2846		*
2847		* <li> The 5ms timestep at 1961 January 1 is taken from 2.58.1 (p87) of
2848		* the 1992 Explanatory Supplement.
2849		*</ol>
2850		*<p>Called:<ul>
2851		* <li>{@link #jauCal2jd} Gregorian calendar to Julian Day number
2852		* </ul>
2853		*<p>@version 20160729
2854		*
2855		* @since Release 20101201
2856		*
2857		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
2858		*/
2859		public static double jauDat(int iy, int im, int id, double fd ) throws JSOFAIllegalParameter, JSOFAInternalError
2860		{
2861
2862		/* Reference dates (MJD) and drift rates (s/day), pre leap seconds */
2863	168	final double drift[][] = {
2864		{ 37300.0, 0.0012960 },
2865		{ 37300.0, 0.0012960 },
2866		{ 37300.0, 0.0012960 },
2867		{ 37665.0, 0.0011232 },
2868		{ 37665.0, 0.0011232 },
2869		{ 38761.0, 0.0012960 },
2870		{ 38761.0, 0.0012960 },
2871		{ 38761.0, 0.0012960 },
2872		{ 38761.0, 0.0012960 },
2873		{ 38761.0, 0.0012960 },
2874		{ 38761.0, 0.0012960 },
2875		{ 38761.0, 0.0012960 },
2876		{ 39126.0, 0.0025920 },
2877		{ 39126.0, 0.0025920 }
2878		};
2879
2880		/* Number of Delta(AT) expressions before leap seconds were introduced */
2881	168	final int NERA1 = drift.length;
2882
2883
2884		/* Number of Delta(AT) changes */
2885	168	final int NDAT = leapSeconds.length;
2886
2887		/* Miscellaneous local variables */
2888		int i, m;
2889		double da, djm;
2890
2891
2892		/* Initialize the result to zero. */
2893	168	double deltat = da = 0.0;
2894
2895		/* If invalid fraction of a day, set error status and give up. */
2896	168	if (fd < 0.0 \|\| fd > 1.0) throw new JSOFAIllegalParameter("bad day fraction", -4);
2897
2898		/* Convert the date into an MJD. */
2899	168	JulianDate jd = jauCal2jd(iy, im, id);
2900	168	djm = jd.djm1;
2901
2902		/* If pre-UTC year, set warning status and give up. */
2903	168	if (iy < leapSeconds[0].iyear) throw new JSOFAInternalError("year before UTC start", 1);
2904
2905		/* If suspiciously late year, set warning status but proceed. */
2906	168	if (iy > IYV + 5) {
2907		}
2908
2909		/* Combine year and month to form a date-ordered integer... */
2910	168	m = 12*iy + im;
2911
2912		/* ...and use it to find the preceding table entry. */
2913	650	for (i = NDAT-1; i >=0; i--) {
2914	650	if (m >= (12 * leapSeconds[i].iyear + leapSeconds[i].month)) break;
2915		}
2916
2917		/* Get the Delta(AT). */
2918	168	da = leapSeconds[i].delat;
2919
2920		/* If pre-1972, adjust for drift. */
2921	168	if (i < NERA1) da += (djm + fd - drift[i][0]) * drift[i][1];
2922
2923		/* Return the Delta(AT) value. */
2924	168	deltat = da;
2925
2926		/* Return the value. */
2927	168	return deltat;
2928
2929		}
2930
2931
2932		/**
2933		* An approximation to TDB-TT, the difference between barycentric
2934		* dynamical time and terrestrial time, for an observer on the Earth.
2935		*
2936		* The different time scales - proper, coordinate and realized - are
2937		* related to each other:
2938		* {@code
2939		* TAI <- physically realized
2940		* :
2941		* offset <- observed (nominally +32.184s)
2942		* :
2943		* TT <- terrestrial time
2944		* :
2945		* rate adjustment (L_G) <- definition of TT
2946		* :
2947		* TCG <- time scale for GCRS
2948		* :
2949		* "periodic" terms <- jauDtdb is an implementation
2950		* :
2951		* rate adjustment (L_C) <- function of solar-system ephemeris
2952		* :
2953		* TCB <- time scale for BCRS
2954		* :
2955		* rate adjustment (-L_B) <- definition of TDB
2956		* :
2957		* TDB <- TCB scaled to track TT
2958		* :
2959		* "periodic" terms <- -jau_DTDB is an approximation
2960		* :
2961		* TT <- terrestrial time
2962		*}
2963		* Adopted values for the various constants can be found in the IERS
2964		* Conventions (McCarthy & Petit 2003).
2965		*
2966		*<p>This function is derived from the International Astronomical Union's
2967		* SOFA (Standards Of Fundamental Astronomy) software collection.
2968		*
2969		*<p>Status: canonical model.
2970		*
2971		*<!-- Given: -->
2972		* @param date1 double date, TDB (Notes 1-3)
2973		* @param date2 double date, TDB (Notes 1-3)
2974		* @param ut double universal time (UT1, fraction of one day)
2975		* @param elong double longitude (east positive, radians)
2976		* @param u double distance from Earth spin axis (km)
2977		* @param v double distance north of equatorial plane (km)
2978		*
2979		* <!-- Returned (function value): -->
2980		* @return @return double TDB-TT (seconds)
2981		*
2982		* <p>Notes:
2983		* <ol>
2984		*
2985		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
2986		* convenient way between the two arguments. For example,
2987		* JD(TT)=2450123.7 could be expressed in any of these ways,
2988		* among others:
2989		*<pre>
2990		* date1 date2
2991		*
2992		* 2450123.7 0.0 (JD method)
2993		* 2451545.0 -1421.3 (J2000 method)
2994		* 2400000.5 50123.2 (MJD method)
2995		* 2450123.5 0.2 (date & time method)
2996		*</pre>
2997		* The JD method is the most natural and convenient to use in
2998		* cases where the loss of several decimal digits of resolution
2999		* is acceptable. The J2000 method is best matched to the way
3000		* the argument is handled internally and will deliver the
3001		* optimum resolution. The MJD method and the date & time methods
3002		* are both good compromises between resolution and convenience.
3003		*
3004		* Although the date is, formally, barycentric dynamical time (TDB),
3005		* the terrestrial dynamical time (TT) can be used with no practical
3006		* effect on the accuracy of the prediction.
3007		*
3008		* <li> TT can be regarded as a coordinate time that is realized as an
3009		* offset of 32.184s from International Atomic Time, TAI. TT is a
3010		* specific linear transformation of geocentric coordinate time TCG,
3011		* which is the time scale for the Geocentric Celestial Reference
3012		* System, GCRS.
3013		*
3014		* <li> TDB is a coordinate time, and is a specific linear transformation
3015		* of barycentric coordinate time TCB, which is the time scale for
3016		* the Barycentric Celestial Reference System, BCRS.
3017		*
3018		* <li> The difference TCG-TCB depends on the masses and positions of the
3019		* bodies of the solar system and the velocity of the Earth. It is
3020		* dominated by a rate difference, the residual being of a periodic
3021		* character. The latter, which is modeled by the present function,
3022		* comprises a main (annual) sinusoidal term of amplitude
3023		* approximately 0.00166 seconds, plus planetary terms up to about
3024		* 20 microseconds, and lunar and diurnal terms up to 2 microseconds.
3025		* These effects come from the changing transverse Doppler effect
3026		* and gravitational red-shift as the observer (on the Earth's
3027		* surface) experiences variations in speed (with respect to the
3028		* BCRS) and gravitational potential.
3029		*
3030		* <li> TDB can be regarded as the same as TCB but with a rate adjustment
3031		* to keep it close to TT, which is convenient for many applications.
3032		* The history of successive attempts to define TDB is set out in
3033		* Resolution 3 adopted by the IAU General Assembly in 2006, which
3034		* defines a fixed TDB(TCB) transformation that is consistent with
3035		* contemporary solar-system ephemerides. Future ephemerides will
3036		* imply slightly changed transformations between TCG and TCB, which
3037		* could introduce a linear drift between TDB and TT; however, any
3038		* such drift is unlikely to exceed 1 nanosecond per century.
3039		*
3040		* <li> The geocentric TDB-TT model used in the present function is that of
3041		* Fairhead & Bretagnon (1990), in its full form. It was originally
3042		* supplied by Fairhead (private communications with P.T.Wallace,
3043		* 1990) as a Fortran subroutine. The present C function contains an
3044		* adaptation of the Fairhead code. The numerical results are
3045		* essentially unaffected by the changes, the differences with
3046		* respect to the Fairhead & Bretagnon original being at the 1e-20 s
3047		* level.
3048		*
3049		* The topocentric part of the model is from Moyer (1981) and
3050		* Murray (1983), with fundamental arguments adapted from
3051		* Simon et al. 1994. It is an approximation to the expression
3052		* ( v / c ) . ( r / c ), where v is the barycentric velocity of
3053		* the Earth, r is the geocentric position of the observer and
3054		* c is the speed of light.
3055		*
3056		* By supplying zeroes for u and v, the topocentric part of the
3057		* model can be nullified, and the function will return the Fairhead
3058		* & Bretagnon result alone.
3059		*
3060		* <li> During the interval 1950-2050, the absolute accuracy is better
3061		* than +/- 3 nanoseconds relative to time ephemerides obtained by
3062		* direct numerical integrations based on the JPL DE405 solar system
3063		* ephemeris.
3064		*
3065		* <li> It must be stressed that the present function is merely a model,
3066		* and that numerical integration of solar-system ephemerides is the
3067		* definitive method for predicting the relationship between TCG and
3068		* TCB and hence between TT and TDB.
3069		*</ol>
3070		*<p>References:
3071		*
3072		* <p>Fairhead, L., & Bretagnon, P., Astron.Astrophys., 229, 240-247
3073		* (1990).
3074		*
3075		* <p>IAU 2006 Resolution 3.
3076		*
3077		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
3078		* IERS Technical Note No. 32, BKG (2004)
3079		*
3080		* <p>Moyer, T.D., Cel.Mech., 23, 33 (1981).
3081		*
3082		* <p>Murray, C.A., Vectorial Astrometry, Adam Hilger (1983).
3083		*
3084		* <p>Seidelmann, P.K. et al., Explanatory Supplement to the
3085		* Astronomical Almanac, Chapter 2, University Science Books (1992).
3086		*
3087		* <p>Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
3088		* Francou, G. & Laskar, J., Astron.Astrophys., 282, 663-683 (1994).
3089		*
3090		*@version 2009 December 17
3091		*
3092		* @since Release 20101201
3093		*
3094		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
3095		*/
3096		public static double jauDtdb(double date1, double date2,
3097		double ut, double elong, double u, double v)
3098		{
3099		double t, tsol, w, elsun, emsun, d, elj, els, wt, w0, w1, w2, w3, w4,
3100		wf, wj;
3101		int j;
3102
3103		/*
3104		* =====================
3105		* Fairhead et al. model
3106		* =====================
3107		*
3108		* 787 sets of three coefficients.
3109		*
3110		* Each set is
3111		* amplitude (microseconds)
3112		* frequency (radians per Julian millennium since J2000.0)
3113		* phase (radians)
3114		*
3115		* Sets 1-474 are the T**0 terms
3116		* " 475-679 " " T**1
3117		* " 680-764 " " T**2
3118		* " 765-784 " " T**3
3119		* " 785-787 " " T**4
3120		*/
3121
3122	2	final double fairhd[][] = {
3123		/* 1, 10 */
3124		{ 1656.674564e-6, 6283.075849991, 6.240054195 },
3125		{ 22.417471e-6, 5753.384884897, 4.296977442 },
3126		{ 13.839792e-6, 12566.151699983, 6.196904410 },
3127		{ 4.770086e-6, 529.690965095, 0.444401603 },
3128		{ 4.676740e-6, 6069.776754553, 4.021195093 },
3129		{ 2.256707e-6, 213.299095438, 5.543113262 },
3130		{ 1.694205e-6, -3.523118349, 5.025132748 },
3131		{ 1.554905e-6, 77713.771467920, 5.198467090 },
3132		{ 1.276839e-6, 7860.419392439, 5.988822341 },
3133		{ 1.193379e-6, 5223.693919802, 3.649823730 },
3134		/* 11, 20 */
3135		{ 1.115322e-6, 3930.209696220, 1.422745069 },
3136		{ 0.794185e-6, 11506.769769794, 2.322313077 },
3137		{ 0.447061e-6, 26.298319800, 3.615796498 },
3138		{ 0.435206e-6, -398.149003408, 4.349338347 },
3139		{ 0.600309e-6, 1577.343542448, 2.678271909 },
3140		{ 0.496817e-6, 6208.294251424, 5.696701824 },
3141		{ 0.486306e-6, 5884.926846583, 0.520007179 },
3142		{ 0.432392e-6, 74.781598567, 2.435898309 },
3143		{ 0.468597e-6, 6244.942814354, 5.866398759 },
3144		{ 0.375510e-6, 5507.553238667, 4.103476804 },
3145		/* 21, 30 */
3146		{ 0.243085e-6, -775.522611324, 3.651837925 },
3147		{ 0.173435e-6, 18849.227549974, 6.153743485 },
3148		{ 0.230685e-6, 5856.477659115, 4.773852582 },
3149		{ 0.203747e-6, 12036.460734888, 4.333987818 },
3150		{ 0.143935e-6, -796.298006816, 5.957517795 },
3151		{ 0.159080e-6, 10977.078804699, 1.890075226 },
3152		{ 0.119979e-6, 38.133035638, 4.551585768 },
3153		{ 0.118971e-6, 5486.777843175, 1.914547226 },
3154		{ 0.116120e-6, 1059.381930189, 0.873504123 },
3155		{ 0.137927e-6, 11790.629088659, 1.135934669 },
3156		/* 31, 40 */
3157		{ 0.098358e-6, 2544.314419883, 0.092793886 },
3158		{ 0.101868e-6, -5573.142801634, 5.984503847 },
3159		{ 0.080164e-6, 206.185548437, 2.095377709 },
3160		{ 0.079645e-6, 4694.002954708, 2.949233637 },
3161		{ 0.062617e-6, 20.775395492, 2.654394814 },
3162		{ 0.075019e-6, 2942.463423292, 4.980931759 },
3163		{ 0.064397e-6, 5746.271337896, 1.280308748 },
3164		{ 0.063814e-6, 5760.498431898, 4.167901731 },
3165		{ 0.048042e-6, 2146.165416475, 1.495846011 },
3166		{ 0.048373e-6, 155.420399434, 2.251573730 },
3167		/* 41, 50 */
3168		{ 0.058844e-6, 426.598190876, 4.839650148 },
3169		{ 0.046551e-6, -0.980321068, 0.921573539 },
3170		{ 0.054139e-6, 17260.154654690, 3.411091093 },
3171		{ 0.042411e-6, 6275.962302991, 2.869567043 },
3172		{ 0.040184e-6, -7.113547001, 3.565975565 },
3173		{ 0.036564e-6, 5088.628839767, 3.324679049 },
3174		{ 0.040759e-6, 12352.852604545, 3.981496998 },
3175		{ 0.036507e-6, 801.820931124, 6.248866009 },
3176		{ 0.036955e-6, 3154.687084896, 5.071801441 },
3177		{ 0.042732e-6, 632.783739313, 5.720622217 },
3178		/* 51, 60 */
3179		{ 0.042560e-6, 161000.685737473, 1.270837679 },
3180		{ 0.040480e-6, 15720.838784878, 2.546610123 },
3181		{ 0.028244e-6, -6286.598968340, 5.069663519 },
3182		{ 0.033477e-6, 6062.663207553, 4.144987272 },
3183		{ 0.034867e-6, 522.577418094, 5.210064075 },
3184		{ 0.032438e-6, 6076.890301554, 0.749317412 },
3185		{ 0.030215e-6, 7084.896781115, 3.389610345 },
3186		{ 0.029247e-6, -71430.695617928, 4.183178762 },
3187		{ 0.033529e-6, 9437.762934887, 2.404714239 },
3188		{ 0.032423e-6, 8827.390269875, 5.541473556 },
3189		/* 61, 70 */
3190		{ 0.027567e-6, 6279.552731642, 5.040846034 },
3191		{ 0.029862e-6, 12139.553509107, 1.770181024 },
3192		{ 0.022509e-6, 10447.387839604, 1.460726241 },
3193		{ 0.020937e-6, 8429.241266467, 0.652303414 },
3194		{ 0.020322e-6, 419.484643875, 3.735430632 },
3195		{ 0.024816e-6, -1194.447010225, 1.087136918 },
3196		{ 0.025196e-6, 1748.016413067, 2.901883301 },
3197		{ 0.021691e-6, 14143.495242431, 5.952658009 },
3198		{ 0.017673e-6, 6812.766815086, 3.186129845 },
3199		{ 0.022567e-6, 6133.512652857, 3.307984806 },
3200		/* 71, 80 */
3201		{ 0.016155e-6, 10213.285546211, 1.331103168 },
3202		{ 0.014751e-6, 1349.867409659, 4.308933301 },
3203		{ 0.015949e-6, -220.412642439, 4.005298270 },
3204		{ 0.015974e-6, -2352.866153772, 6.145309371 },
3205		{ 0.014223e-6, 17789.845619785, 2.104551349 },
3206		{ 0.017806e-6, 73.297125859, 3.475975097 },
3207		{ 0.013671e-6, -536.804512095, 5.971672571 },
3208		{ 0.011942e-6, 8031.092263058, 2.053414715 },
3209		{ 0.014318e-6, 16730.463689596, 3.016058075 },
3210		{ 0.012462e-6, 103.092774219, 1.737438797 },
3211		/* 81, 90 */
3212		{ 0.010962e-6, 3.590428652, 2.196567739 },
3213		{ 0.015078e-6, 19651.048481098, 3.969480770 },
3214		{ 0.010396e-6, 951.718406251, 5.717799605 },
3215		{ 0.011707e-6, -4705.732307544, 2.654125618 },
3216		{ 0.010453e-6, 5863.591206116, 1.913704550 },
3217		{ 0.012420e-6, 4690.479836359, 4.734090399 },
3218		{ 0.011847e-6, 5643.178563677, 5.489005403 },
3219		{ 0.008610e-6, 3340.612426700, 3.661698944 },
3220		{ 0.011622e-6, 5120.601145584, 4.863931876 },
3221		{ 0.010825e-6, 553.569402842, 0.842715011 },
3222		/* 91, 100 */
3223		{ 0.008666e-6, -135.065080035, 3.293406547 },
3224		{ 0.009963e-6, 149.563197135, 4.870690598 },
3225		{ 0.009858e-6, 6309.374169791, 1.061816410 },
3226		{ 0.007959e-6, 316.391869657, 2.465042647 },
3227		{ 0.010099e-6, 283.859318865, 1.942176992 },
3228		{ 0.007147e-6, -242.728603974, 3.661486981 },
3229		{ 0.007505e-6, 5230.807466803, 4.920937029 },
3230		{ 0.008323e-6, 11769.853693166, 1.229392026 },
3231		{ 0.007490e-6, -6256.777530192, 3.658444681 },
3232		{ 0.009370e-6, 149854.400134205, 0.673880395 },
3233		/* 101, 110 */
3234		{ 0.007117e-6, 38.027672636, 5.294249518 },
3235		{ 0.007857e-6, 12168.002696575, 0.525733528 },
3236		{ 0.007019e-6, 6206.809778716, 0.837688810 },
3237		{ 0.006056e-6, 955.599741609, 4.194535082 },
3238		{ 0.008107e-6, 13367.972631107, 3.793235253 },
3239		{ 0.006731e-6, 5650.292110678, 5.639906583 },
3240		{ 0.007332e-6, 36.648562930, 0.114858677 },
3241		{ 0.006366e-6, 4164.311989613, 2.262081818 },
3242		{ 0.006858e-6, 5216.580372801, 0.642063318 },
3243		{ 0.006919e-6, 6681.224853400, 6.018501522 },
3244		/* 111, 120 */
3245		{ 0.006826e-6, 7632.943259650, 3.458654112 },
3246		{ 0.005308e-6, -1592.596013633, 2.500382359 },
3247		{ 0.005096e-6, 11371.704689758, 2.547107806 },
3248		{ 0.004841e-6, 5333.900241022, 0.437078094 },
3249		{ 0.005582e-6, 5966.683980335, 2.246174308 },
3250		{ 0.006304e-6, 11926.254413669, 2.512929171 },
3251		{ 0.006603e-6, 23581.258177318, 5.393136889 },
3252		{ 0.005123e-6, -1.484472708, 2.999641028 },
3253		{ 0.004648e-6, 1589.072895284, 1.275847090 },
3254		{ 0.005119e-6, 6438.496249426, 1.486539246 },
3255		/* 121, 130 */
3256		{ 0.004521e-6, 4292.330832950, 6.140635794 },
3257		{ 0.005680e-6, 23013.539539587, 4.557814849 },
3258		{ 0.005488e-6, -3.455808046, 0.090675389 },
3259		{ 0.004193e-6, 7234.794256242, 4.869091389 },
3260		{ 0.003742e-6, 7238.675591600, 4.691976180 },
3261		{ 0.004148e-6, -110.206321219, 3.016173439 },
3262		{ 0.004553e-6, 11499.656222793, 5.554998314 },
3263		{ 0.004892e-6, 5436.993015240, 1.475415597 },
3264		{ 0.004044e-6, 4732.030627343, 1.398784824 },
3265		{ 0.004164e-6, 12491.370101415, 5.650931916 },
3266		/* 131, 140 */
3267		{ 0.004349e-6, 11513.883316794, 2.181745369 },
3268		{ 0.003919e-6, 12528.018664345, 5.823319737 },
3269		{ 0.003129e-6, 6836.645252834, 0.003844094 },
3270		{ 0.004080e-6, -7058.598461315, 3.690360123 },
3271		{ 0.003270e-6, 76.266071276, 1.517189902 },
3272		{ 0.002954e-6, 6283.143160294, 4.447203799 },
3273		{ 0.002872e-6, 28.449187468, 1.158692983 },
3274		{ 0.002881e-6, 735.876513532, 0.349250250 },
3275		{ 0.003279e-6, 5849.364112115, 4.893384368 },
3276		{ 0.003625e-6, 6209.778724132, 1.473760578 },
3277		/* 141, 150 */
3278		{ 0.003074e-6, 949.175608970, 5.185878737 },
3279		{ 0.002775e-6, 9917.696874510, 1.030026325 },
3280		{ 0.002646e-6, 10973.555686350, 3.918259169 },
3281		{ 0.002575e-6, 25132.303399966, 6.109659023 },
3282		{ 0.003500e-6, 263.083923373, 1.892100742 },
3283		{ 0.002740e-6, 18319.536584880, 4.320519510 },
3284		{ 0.002464e-6, 202.253395174, 4.698203059 },
3285		{ 0.002409e-6, 2.542797281, 5.325009315 },
3286		{ 0.003354e-6, -90955.551694697, 1.942656623 },
3287		{ 0.002296e-6, 6496.374945429, 5.061810696 },
3288		/* 151, 160 */
3289		{ 0.003002e-6, 6172.869528772, 2.797822767 },
3290		{ 0.003202e-6, 27511.467873537, 0.531673101 },
3291		{ 0.002954e-6, -6283.008539689, 4.533471191 },
3292		{ 0.002353e-6, 639.897286314, 3.734548088 },
3293		{ 0.002401e-6, 16200.772724501, 2.605547070 },
3294		{ 0.003053e-6, 233141.314403759, 3.029030662 },
3295		{ 0.003024e-6, 83286.914269554, 2.355556099 },
3296		{ 0.002863e-6, 17298.182327326, 5.240963796 },
3297		{ 0.002103e-6, -7079.373856808, 5.756641637 },
3298		{ 0.002303e-6, 83996.847317911, 2.013686814 },
3299		/* 161, 170 */
3300		{ 0.002303e-6, 18073.704938650, 1.089100410 },
3301		{ 0.002381e-6, 63.735898303, 0.759188178 },
3302		{ 0.002493e-6, 6386.168624210, 0.645026535 },
3303		{ 0.002366e-6, 3.932153263, 6.215885448 },
3304		{ 0.002169e-6, 11015.106477335, 4.845297676 },
3305		{ 0.002397e-6, 6243.458341645, 3.809290043 },
3306		{ 0.002183e-6, 1162.474704408, 6.179611691 },
3307		{ 0.002353e-6, 6246.427287062, 4.781719760 },
3308		{ 0.002199e-6, -245.831646229, 5.956152284 },
3309		{ 0.001729e-6, 3894.181829542, 1.264976635 },
3310		/* 171, 180 */
3311		{ 0.001896e-6, -3128.388765096, 4.914231596 },
3312		{ 0.002085e-6, 35.164090221, 1.405158503 },
3313		{ 0.002024e-6, 14712.317116458, 2.752035928 },
3314		{ 0.001737e-6, 6290.189396992, 5.280820144 },
3315		{ 0.002229e-6, 491.557929457, 1.571007057 },
3316		{ 0.001602e-6, 14314.168113050, 4.203664806 },
3317		{ 0.002186e-6, 454.909366527, 1.402101526 },
3318		{ 0.001897e-6, 22483.848574493, 4.167932508 },
3319		{ 0.001825e-6, -3738.761430108, 0.545828785 },
3320		{ 0.001894e-6, 1052.268383188, 5.817167450 },
3321		/* 181, 190 */
3322		{ 0.001421e-6, 20.355319399, 2.419886601 },
3323		{ 0.001408e-6, 10984.192351700, 2.732084787 },
3324		{ 0.001847e-6, 10873.986030480, 2.903477885 },
3325		{ 0.001391e-6, -8635.942003763, 0.593891500 },
3326		{ 0.001388e-6, -7.046236698, 1.166145902 },
3327		{ 0.001810e-6, -88860.057071188, 0.487355242 },
3328		{ 0.001288e-6, -1990.745017041, 3.913022880 },
3329		{ 0.001297e-6, 23543.230504682, 3.063805171 },
3330		{ 0.001335e-6, -266.607041722, 3.995764039 },
3331		{ 0.001376e-6, 10969.965257698, 5.152914309 },
3332		/* 191, 200 */
3333		{ 0.001745e-6, 244287.600007027, 3.626395673 },
3334		{ 0.001649e-6, 31441.677569757, 1.952049260 },
3335		{ 0.001416e-6, 9225.539273283, 4.996408389 },
3336		{ 0.001238e-6, 4804.209275927, 5.503379738 },
3337		{ 0.001472e-6, 4590.910180489, 4.164913291 },
3338		{ 0.001169e-6, 6040.347246017, 5.841719038 },
3339		{ 0.001039e-6, 5540.085789459, 2.769753519 },
3340		{ 0.001004e-6, -170.672870619, 0.755008103 },
3341		{ 0.001284e-6, 10575.406682942, 5.306538209 },
3342		{ 0.001278e-6, 71.812653151, 4.713486491 },
3343		/* 201, 210 */
3344		{ 0.001321e-6, 18209.330263660, 2.624866359 },
3345		{ 0.001297e-6, 21228.392023546, 0.382603541 },
3346		{ 0.000954e-6, 6282.095528923, 0.882213514 },
3347		{ 0.001145e-6, 6058.731054289, 1.169483931 },
3348		{ 0.000979e-6, 5547.199336460, 5.448375984 },
3349		{ 0.000987e-6, -6262.300454499, 2.656486959 },
3350		{ 0.001070e-6, -154717.609887482, 1.827624012 },
3351		{ 0.000991e-6, 4701.116501708, 4.387001801 },
3352		{ 0.001155e-6, -14.227094002, 3.042700750 },
3353		{ 0.001176e-6, 277.034993741, 3.335519004 },
3354		/* 211, 220 */
3355		{ 0.000890e-6, 13916.019109642, 5.601498297 },
3356		{ 0.000884e-6, -1551.045222648, 1.088831705 },
3357		{ 0.000876e-6, 5017.508371365, 3.969902609 },
3358		{ 0.000806e-6, 15110.466119866, 5.142876744 },
3359		{ 0.000773e-6, -4136.910433516, 0.022067765 },
3360		{ 0.001077e-6, 175.166059800, 1.844913056 },
3361		{ 0.000954e-6, -6284.056171060, 0.968480906 },
3362		{ 0.000737e-6, 5326.786694021, 4.923831588 },
3363		{ 0.000845e-6, -433.711737877, 4.749245231 },
3364		{ 0.000819e-6, 8662.240323563, 5.991247817 },
3365		/* 221, 230 */
3366		{ 0.000852e-6, 199.072001436, 2.189604979 },
3367		{ 0.000723e-6, 17256.631536341, 6.068719637 },
3368		{ 0.000940e-6, 6037.244203762, 6.197428148 },
3369		{ 0.000885e-6, 11712.955318231, 3.280414875 },
3370		{ 0.000706e-6, 12559.038152982, 2.824848947 },
3371		{ 0.000732e-6, 2379.164473572, 2.501813417 },
3372		{ 0.000764e-6, -6127.655450557, 2.236346329 },
3373		{ 0.000908e-6, 131.541961686, 2.521257490 },
3374		{ 0.000907e-6, 35371.887265976, 3.370195967 },
3375		{ 0.000673e-6, 1066.495477190, 3.876512374 },
3376		/* 231, 240 */
3377		{ 0.000814e-6, 17654.780539750, 4.627122566 },
3378		{ 0.000630e-6, 36.027866677, 0.156368499 },
3379		{ 0.000798e-6, 515.463871093, 5.151962502 },
3380		{ 0.000798e-6, 148.078724426, 5.909225055 },
3381		{ 0.000806e-6, 309.278322656, 6.054064447 },
3382		{ 0.000607e-6, -39.617508346, 2.839021623 },
3383		{ 0.000601e-6, 412.371096874, 3.984225404 },
3384		{ 0.000646e-6, 11403.676995575, 3.852959484 },
3385		{ 0.000704e-6, 13521.751441591, 2.300991267 },
3386		{ 0.000603e-6, -65147.619767937, 4.140083146 },
3387		/* 241, 250 */
3388		{ 0.000609e-6, 10177.257679534, 0.437122327 },
3389		{ 0.000631e-6, 5767.611978898, 4.026532329 },
3390		{ 0.000576e-6, 11087.285125918, 4.760293101 },
3391		{ 0.000674e-6, 14945.316173554, 6.270510511 },
3392		{ 0.000726e-6, 5429.879468239, 6.039606892 },
3393		{ 0.000710e-6, 28766.924424484, 5.672617711 },
3394		{ 0.000647e-6, 11856.218651625, 3.397132627 },
3395		{ 0.000678e-6, -5481.254918868, 6.249666675 },
3396		{ 0.000618e-6, 22003.914634870, 2.466427018 },
3397		{ 0.000738e-6, 6134.997125565, 2.242668890 },
3398		/* 251, 260 */
3399		{ 0.000660e-6, 625.670192312, 5.864091907 },
3400		{ 0.000694e-6, 3496.032826134, 2.668309141 },
3401		{ 0.000531e-6, 6489.261398429, 1.681888780 },
3402		{ 0.000611e-6, -143571.324284214, 2.424978312 },
3403		{ 0.000575e-6, 12043.574281889, 4.216492400 },
3404		{ 0.000553e-6, 12416.588502848, 4.772158039 },
3405		{ 0.000689e-6, 4686.889407707, 6.224271088 },
3406		{ 0.000495e-6, 7342.457780181, 3.817285811 },
3407		{ 0.000567e-6, 3634.621024518, 1.649264690 },
3408		{ 0.000515e-6, 18635.928454536, 3.945345892 },
3409		/* 261, 270 */
3410		{ 0.000486e-6, -323.505416657, 4.061673868 },
3411		{ 0.000662e-6, 25158.601719765, 1.794058369 },
3412		{ 0.000509e-6, 846.082834751, 3.053874588 },
3413		{ 0.000472e-6, -12569.674818332, 5.112133338 },
3414		{ 0.000461e-6, 6179.983075773, 0.513669325 },
3415		{ 0.000641e-6, 83467.156352816, 3.210727723 },
3416		{ 0.000520e-6, 10344.295065386, 2.445597761 },
3417		{ 0.000493e-6, 18422.629359098, 1.676939306 },
3418		{ 0.000478e-6, 1265.567478626, 5.487314569 },
3419		{ 0.000472e-6, -18.159247265, 1.999707589 },
3420		/* 271, 280 */
3421		{ 0.000559e-6, 11190.377900137, 5.783236356 },
3422		{ 0.000494e-6, 9623.688276691, 3.022645053 },
3423		{ 0.000463e-6, 5739.157790895, 1.411223013 },
3424		{ 0.000432e-6, 16858.482532933, 1.179256434 },
3425		{ 0.000574e-6, 72140.628666286, 1.758191830 },
3426		{ 0.000484e-6, 17267.268201691, 3.290589143 },
3427		{ 0.000550e-6, 4907.302050146, 0.864024298 },
3428		{ 0.000399e-6, 14.977853527, 2.094441910 },
3429		{ 0.000491e-6, 224.344795702, 0.878372791 },
3430		{ 0.000432e-6, 20426.571092422, 6.003829241 },
3431		/* 281, 290 */
3432		{ 0.000481e-6, 5749.452731634, 4.309591964 },
3433		{ 0.000480e-6, 5757.317038160, 1.142348571 },
3434		{ 0.000485e-6, 6702.560493867, 0.210580917 },
3435		{ 0.000426e-6, 6055.549660552, 4.274476529 },
3436		{ 0.000480e-6, 5959.570433334, 5.031351030 },
3437		{ 0.000466e-6, 12562.628581634, 4.959581597 },
3438		{ 0.000520e-6, 39302.096962196, 4.788002889 },
3439		{ 0.000458e-6, 12132.439962106, 1.880103788 },
3440		{ 0.000470e-6, 12029.347187887, 1.405611197 },
3441		{ 0.000416e-6, -7477.522860216, 1.082356330 },
3442		/* 291, 300 */
3443		{ 0.000449e-6, 11609.862544012, 4.179989585 },
3444		{ 0.000465e-6, 17253.041107690, 0.353496295 },
3445		{ 0.000362e-6, -4535.059436924, 1.583849576 },
3446		{ 0.000383e-6, 21954.157609398, 3.747376371 },
3447		{ 0.000389e-6, 17.252277143, 1.395753179 },
3448		{ 0.000331e-6, 18052.929543158, 0.566790582 },
3449		{ 0.000430e-6, 13517.870106233, 0.685827538 },
3450		{ 0.000368e-6, -5756.908003246, 0.731374317 },
3451		{ 0.000330e-6, 10557.594160824, 3.710043680 },
3452		{ 0.000332e-6, 20199.094959633, 1.652901407 },
3453		/* 301, 310 */
3454		{ 0.000384e-6, 11933.367960670, 5.827781531 },
3455		{ 0.000387e-6, 10454.501386605, 2.541182564 },
3456		{ 0.000325e-6, 15671.081759407, 2.178850542 },
3457		{ 0.000318e-6, 138.517496871, 2.253253037 },
3458		{ 0.000305e-6, 9388.005909415, 0.578340206 },
3459		{ 0.000352e-6, 5749.861766548, 3.000297967 },
3460		{ 0.000311e-6, 6915.859589305, 1.693574249 },
3461		{ 0.000297e-6, 24072.921469776, 1.997249392 },
3462		{ 0.000363e-6, -640.877607382, 5.071820966 },
3463		{ 0.000323e-6, 12592.450019783, 1.072262823 },
3464		/* 311, 320 */
3465		{ 0.000341e-6, 12146.667056108, 4.700657997 },
3466		{ 0.000290e-6, 9779.108676125, 1.812320441 },
3467		{ 0.000342e-6, 6132.028180148, 4.322238614 },
3468		{ 0.000329e-6, 6268.848755990, 3.033827743 },
3469		{ 0.000374e-6, 17996.031168222, 3.388716544 },
3470		{ 0.000285e-6, -533.214083444, 4.687313233 },
3471		{ 0.000338e-6, 6065.844601290, 0.877776108 },
3472		{ 0.000276e-6, 24.298513841, 0.770299429 },
3473		{ 0.000336e-6, -2388.894020449, 5.353796034 },
3474		{ 0.000290e-6, 3097.883822726, 4.075291557 },
3475		/* 321, 330 */
3476		{ 0.000318e-6, 709.933048357, 5.941207518 },
3477		{ 0.000271e-6, 13095.842665077, 3.208912203 },
3478		{ 0.000331e-6, 6073.708907816, 4.007881169 },
3479		{ 0.000292e-6, 742.990060533, 2.714333592 },
3480		{ 0.000362e-6, 29088.811415985, 3.215977013 },
3481		{ 0.000280e-6, 12359.966151546, 0.710872502 },
3482		{ 0.000267e-6, 10440.274292604, 4.730108488 },
3483		{ 0.000262e-6, 838.969287750, 1.327720272 },
3484		{ 0.000250e-6, 16496.361396202, 0.898769761 },
3485		{ 0.000325e-6, 20597.243963041, 0.180044365 },
3486		/* 331, 340 */
3487		{ 0.000268e-6, 6148.010769956, 5.152666276 },
3488		{ 0.000284e-6, 5636.065016677, 5.655385808 },
3489		{ 0.000301e-6, 6080.822454817, 2.135396205 },
3490		{ 0.000294e-6, -377.373607916, 3.708784168 },
3491		{ 0.000236e-6, 2118.763860378, 1.733578756 },
3492		{ 0.000234e-6, 5867.523359379, 5.575209112 },
3493		{ 0.000268e-6, -226858.238553767, 0.069432392 },
3494		{ 0.000265e-6, 167283.761587465, 4.369302826 },
3495		{ 0.000280e-6, 28237.233459389, 5.304829118 },
3496		{ 0.000292e-6, 12345.739057544, 4.096094132 },
3497		/* 341, 350 */
3498		{ 0.000223e-6, 19800.945956225, 3.069327406 },
3499		{ 0.000301e-6, 43232.306658416, 6.205311188 },
3500		{ 0.000264e-6, 18875.525869774, 1.417263408 },
3501		{ 0.000304e-6, -1823.175188677, 3.409035232 },
3502		{ 0.000301e-6, 109.945688789, 0.510922054 },
3503		{ 0.000260e-6, 813.550283960, 2.389438934 },
3504		{ 0.000299e-6, 316428.228673312, 5.384595078 },
3505		{ 0.000211e-6, 5756.566278634, 3.789392838 },
3506		{ 0.000209e-6, 5750.203491159, 1.661943545 },
3507		{ 0.000240e-6, 12489.885628707, 5.684549045 },
3508		/* 351, 360 */
3509		{ 0.000216e-6, 6303.851245484, 3.862942261 },
3510		{ 0.000203e-6, 1581.959348283, 5.549853589 },
3511		{ 0.000200e-6, 5642.198242609, 1.016115785 },
3512		{ 0.000197e-6, -70.849445304, 4.690702525 },
3513		{ 0.000227e-6, 6287.008003254, 2.911891613 },
3514		{ 0.000197e-6, 533.623118358, 1.048982898 },
3515		{ 0.000205e-6, -6279.485421340, 1.829362730 },
3516		{ 0.000209e-6, -10988.808157535, 2.636140084 },
3517		{ 0.000208e-6, -227.526189440, 4.127883842 },
3518		{ 0.000191e-6, 415.552490612, 4.401165650 },
3519		/* 361, 370 */
3520		{ 0.000190e-6, 29296.615389579, 4.175658539 },
3521		{ 0.000264e-6, 66567.485864652, 4.601102551 },
3522		{ 0.000256e-6, -3646.350377354, 0.506364778 },
3523		{ 0.000188e-6, 13119.721102825, 2.032195842 },
3524		{ 0.000185e-6, -209.366942175, 4.694756586 },
3525		{ 0.000198e-6, 25934.124331089, 3.832703118 },
3526		{ 0.000195e-6, 4061.219215394, 3.308463427 },
3527		{ 0.000234e-6, 5113.487598583, 1.716090661 },
3528		{ 0.000188e-6, 1478.866574064, 5.686865780 },
3529		{ 0.000222e-6, 11823.161639450, 1.942386641 },
3530		/* 371, 380 */
3531		{ 0.000181e-6, 10770.893256262, 1.999482059 },
3532		{ 0.000171e-6, 6546.159773364, 1.182807992 },
3533		{ 0.000206e-6, 70.328180442, 5.934076062 },
3534		{ 0.000169e-6, 20995.392966449, 2.169080622 },
3535		{ 0.000191e-6, 10660.686935042, 5.405515999 },
3536		{ 0.000228e-6, 33019.021112205, 4.656985514 },
3537		{ 0.000184e-6, -4933.208440333, 3.327476868 },
3538		{ 0.000220e-6, -135.625325010, 1.765430262 },
3539		{ 0.000166e-6, 23141.558382925, 3.454132746 },
3540		{ 0.000191e-6, 6144.558353121, 5.020393445 },
3541		/* 381, 390 */
3542		{ 0.000180e-6, 6084.003848555, 0.602182191 },
3543		{ 0.000163e-6, 17782.732072784, 4.960593133 },
3544		{ 0.000225e-6, 16460.333529525, 2.596451817 },
3545		{ 0.000222e-6, 5905.702242076, 3.731990323 },
3546		{ 0.000204e-6, 227.476132789, 5.636192701 },
3547		{ 0.000159e-6, 16737.577236597, 3.600691544 },
3548		{ 0.000200e-6, 6805.653268085, 0.868220961 },
3549		{ 0.000187e-6, 11919.140866668, 2.629456641 },
3550		{ 0.000161e-6, 127.471796607, 2.862574720 },
3551		{ 0.000205e-6, 6286.666278643, 1.742882331 },
3552		/* 391, 400 */
3553		{ 0.000189e-6, 153.778810485, 4.812372643 },
3554		{ 0.000168e-6, 16723.350142595, 0.027860588 },
3555		{ 0.000149e-6, 11720.068865232, 0.659721876 },
3556		{ 0.000189e-6, 5237.921013804, 5.245313000 },
3557		{ 0.000143e-6, 6709.674040867, 4.317625647 },
3558		{ 0.000146e-6, 4487.817406270, 4.815297007 },
3559		{ 0.000144e-6, -664.756045130, 5.381366880 },
3560		{ 0.000175e-6, 5127.714692584, 4.728443327 },
3561		{ 0.000162e-6, 6254.626662524, 1.435132069 },
3562		{ 0.000187e-6, 47162.516354635, 1.354371923 },
3563		/* 401, 410 */
3564		{ 0.000146e-6, 11080.171578918, 3.369695406 },
3565		{ 0.000180e-6, -348.924420448, 2.490902145 },
3566		{ 0.000148e-6, 151.047669843, 3.799109588 },
3567		{ 0.000157e-6, 6197.248551160, 1.284375887 },
3568		{ 0.000167e-6, 146.594251718, 0.759969109 },
3569		{ 0.000133e-6, -5331.357443741, 5.409701889 },
3570		{ 0.000154e-6, 95.979227218, 3.366890614 },
3571		{ 0.000148e-6, -6418.140930027, 3.384104996 },
3572		{ 0.000128e-6, -6525.804453965, 3.803419985 },
3573		{ 0.000130e-6, 11293.470674356, 0.939039445 },
3574		/* 411, 420 */
3575		{ 0.000152e-6, -5729.506447149, 0.734117523 },
3576		{ 0.000138e-6, 210.117701700, 2.564216078 },
3577		{ 0.000123e-6, 6066.595360816, 4.517099537 },
3578		{ 0.000140e-6, 18451.078546566, 0.642049130 },
3579		{ 0.000126e-6, 11300.584221356, 3.485280663 },
3580		{ 0.000119e-6, 10027.903195729, 3.217431161 },
3581		{ 0.000151e-6, 4274.518310832, 4.404359108 },
3582		{ 0.000117e-6, 6072.958148291, 0.366324650 },
3583		{ 0.000165e-6, -7668.637425143, 4.298212528 },
3584		{ 0.000117e-6, -6245.048177356, 5.379518958 },
3585		/* 421, 430 */
3586		{ 0.000130e-6, -5888.449964932, 4.527681115 },
3587		{ 0.000121e-6, -543.918059096, 6.109429504 },
3588		{ 0.000162e-6, 9683.594581116, 5.720092446 },
3589		{ 0.000141e-6, 6219.339951688, 0.679068671 },
3590		{ 0.000118e-6, 22743.409379516, 4.881123092 },
3591		{ 0.000129e-6, 1692.165669502, 0.351407289 },
3592		{ 0.000126e-6, 5657.405657679, 5.146592349 },
3593		{ 0.000114e-6, 728.762966531, 0.520791814 },
3594		{ 0.000120e-6, 52.596639600, 0.948516300 },
3595		{ 0.000115e-6, 65.220371012, 3.504914846 },
3596		/* 431, 440 */
3597		{ 0.000126e-6, 5881.403728234, 5.577502482 },
3598		{ 0.000158e-6, 163096.180360983, 2.957128968 },
3599		{ 0.000134e-6, 12341.806904281, 2.598576764 },
3600		{ 0.000151e-6, 16627.370915377, 3.985702050 },
3601		{ 0.000109e-6, 1368.660252845, 0.014730471 },
3602		{ 0.000131e-6, 6211.263196841, 0.085077024 },
3603		{ 0.000146e-6, 5792.741760812, 0.708426604 },
3604		{ 0.000146e-6, -77.750543984, 3.121576600 },
3605		{ 0.000107e-6, 5341.013788022, 0.288231904 },
3606		{ 0.000138e-6, 6281.591377283, 2.797450317 },
3607		/* 441, 450 */
3608		{ 0.000113e-6, -6277.552925684, 2.788904128 },
3609		{ 0.000115e-6, -525.758811831, 5.895222200 },
3610		{ 0.000138e-6, 6016.468808270, 6.096188999 },
3611		{ 0.000139e-6, 23539.707386333, 2.028195445 },
3612		{ 0.000146e-6, -4176.041342449, 4.660008502 },
3613		{ 0.000107e-6, 16062.184526117, 4.066520001 },
3614		{ 0.000142e-6, 83783.548222473, 2.936315115 },
3615		{ 0.000128e-6, 9380.959672717, 3.223844306 },
3616		{ 0.000135e-6, 6205.325306007, 1.638054048 },
3617		{ 0.000101e-6, 2699.734819318, 5.481603249 },
3618		/* 451, 460 */
3619		{ 0.000104e-6, -568.821874027, 2.205734493 },
3620		{ 0.000103e-6, 6321.103522627, 2.440421099 },
3621		{ 0.000119e-6, 6321.208885629, 2.547496264 },
3622		{ 0.000138e-6, 1975.492545856, 2.314608466 },
3623		{ 0.000121e-6, 137.033024162, 4.539108237 },
3624		{ 0.000123e-6, 19402.796952817, 4.538074405 },
3625		{ 0.000119e-6, 22805.735565994, 2.869040566 },
3626		{ 0.000133e-6, 64471.991241142, 6.056405489 },
3627		{ 0.000129e-6, -85.827298831, 2.540635083 },
3628		{ 0.000131e-6, 13613.804277336, 4.005732868 },
3629		/* 461, 470 */
3630		{ 0.000104e-6, 9814.604100291, 1.959967212 },
3631		{ 0.000112e-6, 16097.679950283, 3.589026260 },
3632		{ 0.000123e-6, 2107.034507542, 1.728627253 },
3633		{ 0.000121e-6, 36949.230808424, 6.072332087 },
3634		{ 0.000108e-6, -12539.853380183, 3.716133846 },
3635		{ 0.000113e-6, -7875.671863624, 2.725771122 },
3636		{ 0.000109e-6, 4171.425536614, 4.033338079 },
3637		{ 0.000101e-6, 6247.911759770, 3.441347021 },
3638		{ 0.000113e-6, 7330.728427345, 0.656372122 },
3639		{ 0.000113e-6, 51092.726050855, 2.791483066 },
3640		/* 471, 480 */
3641		{ 0.000106e-6, 5621.842923210, 1.815323326 },
3642		{ 0.000101e-6, 111.430161497, 5.711033677 },
3643		{ 0.000103e-6, 909.818733055, 2.812745443 },
3644		{ 0.000101e-6, 1790.642637886, 1.965746028 },
3645
3646		/* T */
3647		{ 102.156724e-6, 6283.075849991, 4.249032005 },
3648		{ 1.706807e-6, 12566.151699983, 4.205904248 },
3649		{ 0.269668e-6, 213.299095438, 3.400290479 },
3650		{ 0.265919e-6, 529.690965095, 5.836047367 },
3651		{ 0.210568e-6, -3.523118349, 6.262738348 },
3652		{ 0.077996e-6, 5223.693919802, 4.670344204 },
3653		/* 481, 490 */
3654		{ 0.054764e-6, 1577.343542448, 4.534800170 },
3655		{ 0.059146e-6, 26.298319800, 1.083044735 },
3656		{ 0.034420e-6, -398.149003408, 5.980077351 },
3657		{ 0.032088e-6, 18849.227549974, 4.162913471 },
3658		{ 0.033595e-6, 5507.553238667, 5.980162321 },
3659		{ 0.029198e-6, 5856.477659115, 0.623811863 },
3660		{ 0.027764e-6, 155.420399434, 3.745318113 },
3661		{ 0.025190e-6, 5746.271337896, 2.980330535 },
3662		{ 0.022997e-6, -796.298006816, 1.174411803 },
3663		{ 0.024976e-6, 5760.498431898, 2.467913690 },
3664		/* 491, 500 */
3665		{ 0.021774e-6, 206.185548437, 3.854787540 },
3666		{ 0.017925e-6, -775.522611324, 1.092065955 },
3667		{ 0.013794e-6, 426.598190876, 2.699831988 },
3668		{ 0.013276e-6, 6062.663207553, 5.845801920 },
3669		{ 0.011774e-6, 12036.460734888, 2.292832062 },
3670		{ 0.012869e-6, 6076.890301554, 5.333425680 },
3671		{ 0.012152e-6, 1059.381930189, 6.222874454 },
3672		{ 0.011081e-6, -7.113547001, 5.154724984 },
3673		{ 0.010143e-6, 4694.002954708, 4.044013795 },
3674		{ 0.009357e-6, 5486.777843175, 3.416081409 },
3675		/* 501, 510 */
3676		{ 0.010084e-6, 522.577418094, 0.749320262 },
3677		{ 0.008587e-6, 10977.078804699, 2.777152598 },
3678		{ 0.008628e-6, 6275.962302991, 4.562060226 },
3679		{ 0.008158e-6, -220.412642439, 5.806891533 },
3680		{ 0.007746e-6, 2544.314419883, 1.603197066 },
3681		{ 0.007670e-6, 2146.165416475, 3.000200440 },
3682		{ 0.007098e-6, 74.781598567, 0.443725817 },
3683		{ 0.006180e-6, -536.804512095, 1.302642751 },
3684		{ 0.005818e-6, 5088.628839767, 4.827723531 },
3685		{ 0.004945e-6, -6286.598968340, 0.268305170 },
3686		/* 511, 520 */
3687		{ 0.004774e-6, 1349.867409659, 5.808636673 },
3688		{ 0.004687e-6, -242.728603974, 5.154890570 },
3689		{ 0.006089e-6, 1748.016413067, 4.403765209 },
3690		{ 0.005975e-6, -1194.447010225, 2.583472591 },
3691		{ 0.004229e-6, 951.718406251, 0.931172179 },
3692		{ 0.005264e-6, 553.569402842, 2.336107252 },
3693		{ 0.003049e-6, 5643.178563677, 1.362634430 },
3694		{ 0.002974e-6, 6812.766815086, 1.583012668 },
3695		{ 0.003403e-6, -2352.866153772, 2.552189886 },
3696		{ 0.003030e-6, 419.484643875, 5.286473844 },
3697		/* 521, 530 */
3698		{ 0.003210e-6, -7.046236698, 1.863796539 },
3699		{ 0.003058e-6, 9437.762934887, 4.226420633 },
3700		{ 0.002589e-6, 12352.852604545, 1.991935820 },
3701		{ 0.002927e-6, 5216.580372801, 2.319951253 },
3702		{ 0.002425e-6, 5230.807466803, 3.084752833 },
3703		{ 0.002656e-6, 3154.687084896, 2.487447866 },
3704		{ 0.002445e-6, 10447.387839604, 2.347139160 },
3705		{ 0.002990e-6, 4690.479836359, 6.235872050 },
3706		{ 0.002890e-6, 5863.591206116, 0.095197563 },
3707		{ 0.002498e-6, 6438.496249426, 2.994779800 },
3708		/* 531, 540 */
3709		{ 0.001889e-6, 8031.092263058, 3.569003717 },
3710		{ 0.002567e-6, 801.820931124, 3.425611498 },
3711		{ 0.001803e-6, -71430.695617928, 2.192295512 },
3712		{ 0.001782e-6, 3.932153263, 5.180433689 },
3713		{ 0.001694e-6, -4705.732307544, 4.641779174 },
3714		{ 0.001704e-6, -1592.596013633, 3.997097652 },
3715		{ 0.001735e-6, 5849.364112115, 0.417558428 },
3716		{ 0.001643e-6, 8429.241266467, 2.180619584 },
3717		{ 0.001680e-6, 38.133035638, 4.164529426 },
3718		{ 0.002045e-6, 7084.896781115, 0.526323854 },
3719		/* 541, 550 */
3720		{ 0.001458e-6, 4292.330832950, 1.356098141 },
3721		{ 0.001437e-6, 20.355319399, 3.895439360 },
3722		{ 0.001738e-6, 6279.552731642, 0.087484036 },
3723		{ 0.001367e-6, 14143.495242431, 3.987576591 },
3724		{ 0.001344e-6, 7234.794256242, 0.090454338 },
3725		{ 0.001438e-6, 11499.656222793, 0.974387904 },
3726		{ 0.001257e-6, 6836.645252834, 1.509069366 },
3727		{ 0.001358e-6, 11513.883316794, 0.495572260 },
3728		{ 0.001628e-6, 7632.943259650, 4.968445721 },
3729		{ 0.001169e-6, 103.092774219, 2.838496795 },
3730		/* 551, 560 */
3731		{ 0.001162e-6, 4164.311989613, 3.408387778 },
3732		{ 0.001092e-6, 6069.776754553, 3.617942651 },
3733		{ 0.001008e-6, 17789.845619785, 0.286350174 },
3734		{ 0.001008e-6, 639.897286314, 1.610762073 },
3735		{ 0.000918e-6, 10213.285546211, 5.532798067 },
3736		{ 0.001011e-6, -6256.777530192, 0.661826484 },
3737		{ 0.000753e-6, 16730.463689596, 3.905030235 },
3738		{ 0.000737e-6, 11926.254413669, 4.641956361 },
3739		{ 0.000694e-6, 3340.612426700, 2.111120332 },
3740		{ 0.000701e-6, 3894.181829542, 2.760823491 },
3741		/* 561, 570 */
3742		{ 0.000689e-6, -135.065080035, 4.768800780 },
3743		{ 0.000700e-6, 13367.972631107, 5.760439898 },
3744		{ 0.000664e-6, 6040.347246017, 1.051215840 },
3745		{ 0.000654e-6, 5650.292110678, 4.911332503 },
3746		{ 0.000788e-6, 6681.224853400, 4.699648011 },
3747		{ 0.000628e-6, 5333.900241022, 5.024608847 },
3748		{ 0.000755e-6, -110.206321219, 4.370971253 },
3749		{ 0.000628e-6, 6290.189396992, 3.660478857 },
3750		{ 0.000635e-6, 25132.303399966, 4.121051532 },
3751		{ 0.000534e-6, 5966.683980335, 1.173284524 },
3752		/* 571, 580 */
3753		{ 0.000543e-6, -433.711737877, 0.345585464 },
3754		{ 0.000517e-6, -1990.745017041, 5.414571768 },
3755		{ 0.000504e-6, 5767.611978898, 2.328281115 },
3756		{ 0.000485e-6, 5753.384884897, 1.685874771 },
3757		{ 0.000463e-6, 7860.419392439, 5.297703006 },
3758		{ 0.000604e-6, 515.463871093, 0.591998446 },
3759		{ 0.000443e-6, 12168.002696575, 4.830881244 },
3760		{ 0.000570e-6, 199.072001436, 3.899190272 },
3761		{ 0.000465e-6, 10969.965257698, 0.476681802 },
3762		{ 0.000424e-6, -7079.373856808, 1.112242763 },
3763		/* 581, 590 */
3764		{ 0.000427e-6, 735.876513532, 1.994214480 },
3765		{ 0.000478e-6, -6127.655450557, 3.778025483 },
3766		{ 0.000414e-6, 10973.555686350, 5.441088327 },
3767		{ 0.000512e-6, 1589.072895284, 0.107123853 },
3768		{ 0.000378e-6, 10984.192351700, 0.915087231 },
3769		{ 0.000402e-6, 11371.704689758, 4.107281715 },
3770		{ 0.000453e-6, 9917.696874510, 1.917490952 },
3771		{ 0.000395e-6, 149.563197135, 2.763124165 },
3772		{ 0.000371e-6, 5739.157790895, 3.112111866 },
3773		{ 0.000350e-6, 11790.629088659, 0.440639857 },
3774		/* 591, 600 */
3775		{ 0.000356e-6, 6133.512652857, 5.444568842 },
3776		{ 0.000344e-6, 412.371096874, 5.676832684 },
3777		{ 0.000383e-6, 955.599741609, 5.559734846 },
3778		{ 0.000333e-6, 6496.374945429, 0.261537984 },
3779		{ 0.000340e-6, 6055.549660552, 5.975534987 },
3780		{ 0.000334e-6, 1066.495477190, 2.335063907 },
3781		{ 0.000399e-6, 11506.769769794, 5.321230910 },
3782		{ 0.000314e-6, 18319.536584880, 2.313312404 },
3783		{ 0.000424e-6, 1052.268383188, 1.211961766 },
3784		{ 0.000307e-6, 63.735898303, 3.169551388 },
3785		/* 601, 610 */
3786		{ 0.000329e-6, 29.821438149, 6.106912080 },
3787		{ 0.000357e-6, 6309.374169791, 4.223760346 },
3788		{ 0.000312e-6, -3738.761430108, 2.180556645 },
3789		{ 0.000301e-6, 309.278322656, 1.499984572 },
3790		{ 0.000268e-6, 12043.574281889, 2.447520648 },
3791		{ 0.000257e-6, 12491.370101415, 3.662331761 },
3792		{ 0.000290e-6, 625.670192312, 1.272834584 },
3793		{ 0.000256e-6, 5429.879468239, 1.913426912 },
3794		{ 0.000339e-6, 3496.032826134, 4.165930011 },
3795		{ 0.000283e-6, 3930.209696220, 4.325565754 },
3796		/* 611, 620 */
3797		{ 0.000241e-6, 12528.018664345, 3.832324536 },
3798		{ 0.000304e-6, 4686.889407707, 1.612348468 },
3799		{ 0.000259e-6, 16200.772724501, 3.470173146 },
3800		{ 0.000238e-6, 12139.553509107, 1.147977842 },
3801		{ 0.000236e-6, 6172.869528772, 3.776271728 },
3802		{ 0.000296e-6, -7058.598461315, 0.460368852 },
3803		{ 0.000306e-6, 10575.406682942, 0.554749016 },
3804		{ 0.000251e-6, 17298.182327326, 0.834332510 },
3805		{ 0.000290e-6, 4732.030627343, 4.759564091 },
3806		{ 0.000261e-6, 5884.926846583, 0.298259862 },
3807		/* 621, 630 */
3808		{ 0.000249e-6, 5547.199336460, 3.749366406 },
3809		{ 0.000213e-6, 11712.955318231, 5.415666119 },
3810		{ 0.000223e-6, 4701.116501708, 2.703203558 },
3811		{ 0.000268e-6, -640.877607382, 0.283670793 },
3812		{ 0.000209e-6, 5636.065016677, 1.238477199 },
3813		{ 0.000193e-6, 10177.257679534, 1.943251340 },
3814		{ 0.000182e-6, 6283.143160294, 2.456157599 },
3815		{ 0.000184e-6, -227.526189440, 5.888038582 },
3816		{ 0.000182e-6, -6283.008539689, 0.241332086 },
3817		{ 0.000228e-6, -6284.056171060, 2.657323816 },
3818		/* 631, 640 */
3819		{ 0.000166e-6, 7238.675591600, 5.930629110 },
3820		{ 0.000167e-6, 3097.883822726, 5.570955333 },
3821		{ 0.000159e-6, -323.505416657, 5.786670700 },
3822		{ 0.000154e-6, -4136.910433516, 1.517805532 },
3823		{ 0.000176e-6, 12029.347187887, 3.139266834 },
3824		{ 0.000167e-6, 12132.439962106, 3.556352289 },
3825		{ 0.000153e-6, 202.253395174, 1.463313961 },
3826		{ 0.000157e-6, 17267.268201691, 1.586837396 },
3827		{ 0.000142e-6, 83996.847317911, 0.022670115 },
3828		{ 0.000152e-6, 17260.154654690, 0.708528947 },
3829		/* 641, 650 */
3830		{ 0.000144e-6, 6084.003848555, 5.187075177 },
3831		{ 0.000135e-6, 5756.566278634, 1.993229262 },
3832		{ 0.000134e-6, 5750.203491159, 3.457197134 },
3833		{ 0.000144e-6, 5326.786694021, 6.066193291 },
3834		{ 0.000160e-6, 11015.106477335, 1.710431974 },
3835		{ 0.000133e-6, 3634.621024518, 2.836451652 },
3836		{ 0.000134e-6, 18073.704938650, 5.453106665 },
3837		{ 0.000134e-6, 1162.474704408, 5.326898811 },
3838		{ 0.000128e-6, 5642.198242609, 2.511652591 },
3839		{ 0.000160e-6, 632.783739313, 5.628785365 },
3840		/* 651, 660 */
3841		{ 0.000132e-6, 13916.019109642, 0.819294053 },
3842		{ 0.000122e-6, 14314.168113050, 5.677408071 },
3843		{ 0.000125e-6, 12359.966151546, 5.251984735 },
3844		{ 0.000121e-6, 5749.452731634, 2.210924603 },
3845		{ 0.000136e-6, -245.831646229, 1.646502367 },
3846		{ 0.000120e-6, 5757.317038160, 3.240883049 },
3847		{ 0.000134e-6, 12146.667056108, 3.059480037 },
3848		{ 0.000137e-6, 6206.809778716, 1.867105418 },
3849		{ 0.000141e-6, 17253.041107690, 2.069217456 },
3850		{ 0.000129e-6, -7477.522860216, 2.781469314 },
3851		/* 661, 670 */
3852		{ 0.000116e-6, 5540.085789459, 4.281176991 },
3853		{ 0.000116e-6, 9779.108676125, 3.320925381 },
3854		{ 0.000129e-6, 5237.921013804, 3.497704076 },
3855		{ 0.000113e-6, 5959.570433334, 0.983210840 },
3856		{ 0.000122e-6, 6282.095528923, 2.674938860 },
3857		{ 0.000140e-6, -11.045700264, 4.957936982 },
3858		{ 0.000108e-6, 23543.230504682, 1.390113589 },
3859		{ 0.000106e-6, -12569.674818332, 0.429631317 },
3860		{ 0.000110e-6, -266.607041722, 5.501340197 },
3861		{ 0.000115e-6, 12559.038152982, 4.691456618 },
3862		/* 671, 680 */
3863		{ 0.000134e-6, -2388.894020449, 0.577313584 },
3864		{ 0.000109e-6, 10440.274292604, 6.218148717 },
3865		{ 0.000102e-6, -543.918059096, 1.477842615 },
3866		{ 0.000108e-6, 21228.392023546, 2.237753948 },
3867		{ 0.000101e-6, -4535.059436924, 3.100492232 },
3868		{ 0.000103e-6, 76.266071276, 5.594294322 },
3869		{ 0.000104e-6, 949.175608970, 5.674287810 },
3870		{ 0.000101e-6, 13517.870106233, 2.196632348 },
3871		{ 0.000100e-6, 11933.367960670, 4.056084160 },
3872
3873		/* T^2 */
3874		{ 4.322990e-6, 6283.075849991, 2.642893748 },
3875		/* 681, 690 */
3876		{ 0.406495e-6, 0.000000000, 4.712388980 },
3877		{ 0.122605e-6, 12566.151699983, 2.438140634 },
3878		{ 0.019476e-6, 213.299095438, 1.642186981 },
3879		{ 0.016916e-6, 529.690965095, 4.510959344 },
3880		{ 0.013374e-6, -3.523118349, 1.502210314 },
3881		{ 0.008042e-6, 26.298319800, 0.478549024 },
3882		{ 0.007824e-6, 155.420399434, 5.254710405 },
3883		{ 0.004894e-6, 5746.271337896, 4.683210850 },
3884		{ 0.004875e-6, 5760.498431898, 0.759507698 },
3885		{ 0.004416e-6, 5223.693919802, 6.028853166 },
3886		/* 691, 700 */
3887		{ 0.004088e-6, -7.113547001, 0.060926389 },
3888		{ 0.004433e-6, 77713.771467920, 3.627734103 },
3889		{ 0.003277e-6, 18849.227549974, 2.327912542 },
3890		{ 0.002703e-6, 6062.663207553, 1.271941729 },
3891		{ 0.003435e-6, -775.522611324, 0.747446224 },
3892		{ 0.002618e-6, 6076.890301554, 3.633715689 },
3893		{ 0.003146e-6, 206.185548437, 5.647874613 },
3894		{ 0.002544e-6, 1577.343542448, 6.232904270 },
3895		{ 0.002218e-6, -220.412642439, 1.309509946 },
3896		{ 0.002197e-6, 5856.477659115, 2.407212349 },
3897		/* 701, 710 */
3898		{ 0.002897e-6, 5753.384884897, 5.863842246 },
3899		{ 0.001766e-6, 426.598190876, 0.754113147 },
3900		{ 0.001738e-6, -796.298006816, 2.714942671 },
3901		{ 0.001695e-6, 522.577418094, 2.629369842 },
3902		{ 0.001584e-6, 5507.553238667, 1.341138229 },
3903		{ 0.001503e-6, -242.728603974, 0.377699736 },
3904		{ 0.001552e-6, -536.804512095, 2.904684667 },
3905		{ 0.001370e-6, -398.149003408, 1.265599125 },
3906		{ 0.001889e-6, -5573.142801634, 4.413514859 },
3907		{ 0.001722e-6, 6069.776754553, 2.445966339 },
3908		/* 711, 720 */
3909		{ 0.001124e-6, 1059.381930189, 5.041799657 },
3910		{ 0.001258e-6, 553.569402842, 3.849557278 },
3911		{ 0.000831e-6, 951.718406251, 2.471094709 },
3912		{ 0.000767e-6, 4694.002954708, 5.363125422 },
3913		{ 0.000756e-6, 1349.867409659, 1.046195744 },
3914		{ 0.000775e-6, -11.045700264, 0.245548001 },
3915		{ 0.000597e-6, 2146.165416475, 4.543268798 },
3916		{ 0.000568e-6, 5216.580372801, 4.178853144 },
3917		{ 0.000711e-6, 1748.016413067, 5.934271972 },
3918		{ 0.000499e-6, 12036.460734888, 0.624434410 },
3919		/* 721, 730 */
3920		{ 0.000671e-6, -1194.447010225, 4.136047594 },
3921		{ 0.000488e-6, 5849.364112115, 2.209679987 },
3922		{ 0.000621e-6, 6438.496249426, 4.518860804 },
3923		{ 0.000495e-6, -6286.598968340, 1.868201275 },
3924		{ 0.000456e-6, 5230.807466803, 1.271231591 },
3925		{ 0.000451e-6, 5088.628839767, 0.084060889 },
3926		{ 0.000435e-6, 5643.178563677, 3.324456609 },
3927		{ 0.000387e-6, 10977.078804699, 4.052488477 },
3928		{ 0.000547e-6, 161000.685737473, 2.841633844 },
3929		{ 0.000522e-6, 3154.687084896, 2.171979966 },
3930		/* 731, 740 */
3931		{ 0.000375e-6, 5486.777843175, 4.983027306 },
3932		{ 0.000421e-6, 5863.591206116, 4.546432249 },
3933		{ 0.000439e-6, 7084.896781115, 0.522967921 },
3934		{ 0.000309e-6, 2544.314419883, 3.172606705 },
3935		{ 0.000347e-6, 4690.479836359, 1.479586566 },
3936		{ 0.000317e-6, 801.820931124, 3.553088096 },
3937		{ 0.000262e-6, 419.484643875, 0.606635550 },
3938		{ 0.000248e-6, 6836.645252834, 3.014082064 },
3939		{ 0.000245e-6, -1592.596013633, 5.519526220 },
3940		{ 0.000225e-6, 4292.330832950, 2.877956536 },
3941		/* 741, 750 */
3942		{ 0.000214e-6, 7234.794256242, 1.605227587 },
3943		{ 0.000205e-6, 5767.611978898, 0.625804796 },
3944		{ 0.000180e-6, 10447.387839604, 3.499954526 },
3945		{ 0.000229e-6, 199.072001436, 5.632304604 },
3946		{ 0.000214e-6, 639.897286314, 5.960227667 },
3947		{ 0.000175e-6, -433.711737877, 2.162417992 },
3948		{ 0.000209e-6, 515.463871093, 2.322150893 },
3949		{ 0.000173e-6, 6040.347246017, 2.556183691 },
3950		{ 0.000184e-6, 6309.374169791, 4.732296790 },
3951		{ 0.000227e-6, 149854.400134205, 5.385812217 },
3952		/* 751, 760 */
3953		{ 0.000154e-6, 8031.092263058, 5.120720920 },
3954		{ 0.000151e-6, 5739.157790895, 4.815000443 },
3955		{ 0.000197e-6, 7632.943259650, 0.222827271 },
3956		{ 0.000197e-6, 74.781598567, 3.910456770 },
3957		{ 0.000138e-6, 6055.549660552, 1.397484253 },
3958		{ 0.000149e-6, -6127.655450557, 5.333727496 },
3959		{ 0.000137e-6, 3894.181829542, 4.281749907 },
3960		{ 0.000135e-6, 9437.762934887, 5.979971885 },
3961		{ 0.000139e-6, -2352.866153772, 4.715630782 },
3962		{ 0.000142e-6, 6812.766815086, 0.513330157 },
3963		/* 761, 770 */
3964		{ 0.000120e-6, -4705.732307544, 0.194160689 },
3965		{ 0.000131e-6, -71430.695617928, 0.000379226 },
3966		{ 0.000124e-6, 6279.552731642, 2.122264908 },
3967		{ 0.000108e-6, -6256.777530192, 0.883445696 },
3968
3969		/* T^3 */
3970		{ 0.143388e-6, 6283.075849991, 1.131453581 },
3971		{ 0.006671e-6, 12566.151699983, 0.775148887 },
3972		{ 0.001480e-6, 155.420399434, 0.480016880 },
3973		{ 0.000934e-6, 213.299095438, 6.144453084 },
3974		{ 0.000795e-6, 529.690965095, 2.941595619 },
3975		{ 0.000673e-6, 5746.271337896, 0.120415406 },
3976		/* 771, 780 */
3977		{ 0.000672e-6, 5760.498431898, 5.317009738 },
3978		{ 0.000389e-6, -220.412642439, 3.090323467 },
3979		{ 0.000373e-6, 6062.663207553, 3.003551964 },
3980		{ 0.000360e-6, 6076.890301554, 1.918913041 },
3981		{ 0.000316e-6, -21.340641002, 5.545798121 },
3982		{ 0.000315e-6, -242.728603974, 1.884932563 },
3983		{ 0.000278e-6, 206.185548437, 1.266254859 },
3984		{ 0.000238e-6, -536.804512095, 4.532664830 },
3985		{ 0.000185e-6, 522.577418094, 4.578313856 },
3986		{ 0.000245e-6, 18849.227549974, 0.587467082 },
3987		/* 781, 787 */
3988		{ 0.000180e-6, 426.598190876, 5.151178553 },
3989		{ 0.000200e-6, 553.569402842, 5.355983739 },
3990		{ 0.000141e-6, 5223.693919802, 1.336556009 },
3991		{ 0.000104e-6, 5856.477659115, 4.239842759 },
3992
3993		/* T^4 */
3994		{ 0.003826e-6, 6283.075849991, 5.705257275 },
3995		{ 0.000303e-6, 12566.151699983, 5.407132842 },
3996		{ 0.000209e-6, 155.420399434, 1.989815753 }
3997		};
3998
3999
4000		/* Time since J2000.0 in Julian millennia. */
4001	2	t = ((date1 - DJ00) + date2) / DJM;
4002
4003		/* ================= */
4004		/* Topocentric terms */
4005		/* ================= */
4006
4007		/* Convert UT to local solar time in radians. */
4008	2	tsol = fmod(ut, 1.0) * D2PI + elong;
4009
4010		/* FUNDAMENTAL ARGUMENTS: Simon et al. 1994. */
4011
4012		/* Combine time argument (millennia) with deg/arcsec factor. */
4013	2	w = t / 3600.0;
4014
4015		/* Sun Mean Longitude. */
4016	2	elsun = fmod(280.46645683 + 1296027711.03429 * w, 360.0) * DD2R;
4017
4018		/* Sun Mean Anomaly. */
4019	2	emsun = fmod(357.52910918 + 1295965810.481 * w, 360.0) * DD2R;
4020
4021		/* Mean Elongation of Moon from Sun. */
4022	2	d = fmod(297.85019547 + 16029616012.090 * w, 360.0) * DD2R;
4023
4024		/* Mean Longitude of Jupiter. */
4025	2	elj = fmod(34.35151874 + 109306899.89453 * w, 360.0) * DD2R;
4026
4027		/* Mean Longitude of Saturn. */
4028	2	els = fmod(50.07744430 + 44046398.47038 * w, 360.0) * DD2R;
4029
4030		/* TOPOCENTRIC TERMS: Moyer 1981 and Murray 1983. */
4031	2	wt = + 0.00029e-10 * u * sin(tsol + elsun - els)
4032	2	+ 0.00100e-10 * u * sin(tsol - 2.0 * emsun)
4033	2	+ 0.00133e-10 * u * sin(tsol - d)
4034	2	+ 0.00133e-10 * u * sin(tsol + elsun - elj)
4035	2	- 0.00229e-10 * u * sin(tsol + 2.0 * elsun + emsun)
4036	2	- 0.02200e-10 * v * cos(elsun + emsun)
4037	2	+ 0.05312e-10 * u * sin(tsol - emsun)
4038	2	- 0.13677e-10 * u * sin(tsol + 2.0 * elsun)
4039	2	- 1.31840e-10 * v * cos(elsun)
4040	2	+ 3.17679e-10 * u * sin(tsol);
4041
4042		/* ===================== */
4043		/* Fairhead et al. model */
4044		/* ===================== */
4045
4046		/* T*0 /
4047	2	w0 = 0;
4048	950	for (j = 473; j >= 0; j--) {
4049	948	w0 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4050		}
4051
4052		/* T*1 /
4053	2	w1 = 0;
4054	412	for (j = 678; j >= 474; j--) {
4055	410	w1 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4056		}
4057
4058		/* T*2 /
4059	2	w2 = 0;
4060	172	for (j = 763; j >= 679; j--) {
4061	170	w2 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4062		}
4063
4064		/* T*3 /
4065	2	w3 = 0;
4066	42	for (j = 783; j >= 764; j--) {
4067	40	w3 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4068		}
4069
4070		/* T*4 /
4071	2	w4 = 0;
4072	8	for (j = 786; j >= 784; j--) {
4073	6	w4 += fairhd[j][0] * sin(fairhd[j][1] * t + fairhd[j][2]);
4074		}
4075
4076		/* Multiply by powers of T and combine. */
4077	2	wf = t * (t * (t * (t * w4 + w3) + w2) + w1) + w0;
4078
4079		/* Adjustments to use JPL planetary masses instead of IAU. */
4080	2	wj = 0.00065e-6 * sin(6069.776754 * t + 4.021194) +
4081	2	0.00033e-6 * sin( 213.299095 * t + 5.543132) +
4082	2	(-0.00196e-6 * sin(6208.294251 * t + 5.696701)) +
4083	2	(-0.00173e-6 * sin( 74.781599 * t + 2.435900)) +
4084		0.03638e-6 * t * t;
4085
4086		/* ============ */
4087		/* Final result */
4088		/* ============ */
4089
4090		/* TDB-TT in seconds. */
4091	2	w = wt + wf + wj;
4092
4093	2	return w;
4094
4095		}
4096
4097
4098		/**
4099		* The equation of the equinoxes, compatible with IAU 2000 resolutions,
4100		* given the nutation in longitude and the mean obliquity.
4101		*
4102		*<p>This function is derived from the International Astronomical Union's
4103		* SOFA (Standards Of Fundamental Astronomy) software collection.
4104		*
4105		*<p>Status: canonical model.
4106		*
4107		*<!-- Given: -->
4108		* @param date1 double TT as a 2-part Julian Date (Note 1)
4109		* @param date2 double TT as a 2-part Julian Date (Note 1)
4110		* @param epsa double mean obliquity (Note 2)
4111		* @param dpsi double nutation in longitude (Note 3)
4112		*
4113		* <!-- Returned (function value): -->
4114		* @return double equation of the equinoxes (Note 4)
4115		*
4116		* <p>Notes:
4117		* <ol>
4118		*
4119		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
4120		* convenient way between the two arguments. For example,
4121		* JD(TT)=2450123.7 could be expressed in any of these ways,
4122		* among others:
4123		*<pre>
4124		* date1 date2
4125		*
4126		* 2450123.7 0.0 (JD method)
4127		* 2451545.0 -1421.3 (J2000 method)
4128		* 2400000.5 50123.2 (MJD method)
4129		* 2450123.5 0.2 (date & time method)
4130		*</pre>
4131		* The JD method is the most natural and convenient to use in
4132		* cases where the loss of several decimal digits of resolution
4133		* is acceptable. The J2000 method is best matched to the way
4134		* the argument is handled internally and will deliver the
4135		* optimum resolution. The MJD method and the date & time methods
4136		* are both good compromises between resolution and convenience.
4137		*
4138		* <li> The obliquity, in radians, is mean of date.
4139		*
4140		* <li> The result, which is in radians, operates in the following sense:
4141		*
4142		* Greenwich apparent ST = GMST + equation of the equinoxes
4143		*
4144		* <li> The result is compatible with the IAU 2000 resolutions. For
4145		* further details, see IERS Conventions 2003 and Capitaine et al.
4146		* (2002).
4147		*</ol>
4148		*<p>Called:<ul>
4149		* <li>{@link #jauEect00} equation of the equinoxes complementary terms
4150		* </ul>
4151		*<p>
4152		*
4153		* <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4154		* implement the IAU 2000 definition of UT1", Astronomy &
4155		* Astrophysics, 406, 1135-1149 (2003)
4156		*
4157		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4158		* IERS Technical Note No. 32, BKG (2004)
4159		*
4160		*@version 2008 May 16
4161		*
4162		* @since Release 20101201
4163		*
4164		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4165		*/
4166		public static double jauEe00(double date1, double date2, double epsa, double dpsi)
4167		{
4168		double ee;
4169
4170
4171		/* Equation of the equinoxes. */
4172	12	ee = dpsi * cos(epsa) + jauEect00(date1, date2);
4173
4174	12	return ee;
4175
4176		}
4177
4178
4179		/**
4180		* Equation of the equinoxes, compatible with IAU 2000 resolutions.
4181		*
4182		*<p>This function is derived from the International Astronomical Union's
4183		* SOFA (Standards Of Fundamental Astronomy) software collection.
4184		*
4185		*<p>Status: support function.
4186		*
4187		*<!-- Given: -->
4188		* @param date1 double TT as a 2-part Julian Date (Note 1)
4189		* @param date2 double TT as a 2-part Julian Date (Note 1)
4190		*
4191		* <!-- Returned (function value): -->
4192		* @return double equation of the equinoxes (Note 2)
4193		*
4194		* <p>Notes:
4195		* <ol>
4196		*
4197		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
4198		* convenient way between the two arguments. For example,
4199		* JD(TT)=2450123.7 could be expressed in any of these ways,
4200		* among others:
4201		*<pre>
4202		* date1 date2
4203		*
4204		* 2450123.7 0.0 (JD method)
4205		* 2451545.0 -1421.3 (J2000 method)
4206		* 2400000.5 50123.2 (MJD method)
4207		* 2450123.5 0.2 (date & time method)
4208		*</pre>
4209		* The JD method is the most natural and convenient to use in
4210		* cases where the loss of several decimal digits of resolution
4211		* is acceptable. The J2000 method is best matched to the way
4212		* the argument is handled internally and will deliver the
4213		* optimum resolution. The MJD method and the date & time methods
4214		* are both good compromises between resolution and convenience.
4215		*
4216		* <li> The result, which is in radians, operates in the following sense:
4217		*
4218		* Greenwich apparent ST = GMST + equation of the equinoxes
4219		*
4220		* <li> The result is compatible with the IAU 2000 resolutions. For
4221		* further details, see IERS Conventions 2003 and Capitaine et al.
4222		* (2002).
4223		*</ol>
4224		*<p>Called:<ul>
4225		* <li>{@link #jauPr00} IAU 2000 precession adjustments
4226		* <li>{@link #jauObl80} mean obliquity, IAU 1980
4227		* <li>{@link #jauNut00a} nutation, IAU 2000A
4228		* <li>{@link #jauEe00} equation of the equinoxes, IAU 2000
4229		* </ul>
4230		*<p>References:
4231		*
4232		* <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4233		* implement the IAU 2000 definition of UT1", Astronomy &
4234		* Astrophysics, 406, 1135-1149 (2003).
4235		*
4236		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4237		* IERS Technical Note No. 32, BKG (2004).
4238		*
4239		*@version 2008 May 16
4240		*
4241		* @since Release 20101201
4242		*
4243		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4244		*/
4245		public static double jauEe00a(double date1, double date2)
4246		{
4247		double epsa, ee;
4248
4249
4250		/* IAU 2000 precession-rate adjustments. */
4251	4	PrecessionDeltaTerms nutd = jauPr00(date1, date2);
4252
4253		/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
4254	4	epsa = jauObl80(date1, date2) + nutd.depspr;
4255
4256		/* Nutation in longitude. */
4257	4	NutationTerms nut = jauNut00a(date1, date2);
4258
4259		/* Equation of the equinoxes. */
4260	4	ee = jauEe00(date1, date2, epsa, nut.dpsi);
4261
4262	4	return ee;
4263
4264		}
4265
4266
4267		/**
4268		* Equation of the equinoxes, compatible with IAU 2000 resolutions but
4269		* using the truncated nutation model IAU 2000B.
4270		*
4271		*<p>This function is derived from the International Astronomical Union's
4272		* SOFA (Standards Of Fundamental Astronomy) software collection.
4273		*
4274		*<p>Status: support function.
4275		*
4276		*<!-- Given: -->
4277		* @param date1 double TT as a 2-part Julian Date (Note 1)
4278		* @param date2 double TT as a 2-part Julian Date (Note 1)
4279		*
4280		* <!-- Returned (function value): -->
4281		* @return double equation of the equinoxes (Note 2)
4282		*
4283		* <p>Notes:
4284		* <ol>
4285		*
4286		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
4287		* convenient way between the two arguments. For example,
4288		* JD(TT)=2450123.7 could be expressed in any of these ways,
4289		* among others:
4290		*<pre>
4291		* date1 date2
4292		*
4293		* 2450123.7 0.0 (JD method)
4294		* 2451545.0 -1421.3 (J2000 method)
4295		* 2400000.5 50123.2 (MJD method)
4296		* 2450123.5 0.2 (date & time method)
4297		*</pre>
4298		* The JD method is the most natural and convenient to use in
4299		* cases where the loss of several decimal digits of resolution
4300		* is acceptable. The J2000 method is best matched to the way
4301		* the argument is handled internally and will deliver the
4302		* optimum resolution. The MJD method and the date & time methods
4303		* are both good compromises between resolution and convenience.
4304		*
4305		* <li> The result, which is in radians, operates in the following sense:
4306		*
4307		* Greenwich apparent ST = GMST + equation of the equinoxes
4308		*
4309		* <li> The result is compatible with the IAU 2000 resolutions except
4310		* that accuracy has been compromised for the sake of speed. For
4311		* further details, see McCarthy & Luzum (2001), IERS Conventions
4312		* 2003 and Capitaine et al. (2003).
4313		*</ol>
4314		*<p>Called:<ul>
4315		* <li>{@link #jauPr00} IAU 2000 precession adjustments
4316		* <li>{@link #jauObl80} mean obliquity, IAU 1980
4317		* <li>{@link #jauNut00b} nutation, IAU 2000B
4318		* <li>{@link #jauEe00} equation of the equinoxes, IAU 2000
4319		* </ul>
4320		*<p>
4321		*
4322		* <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4323		* implement the IAU 2000 definition of UT1", Astronomy &
4324		* Astrophysics, 406, 1135-1149 (2003)
4325		*
4326		* <p>McCarthy, D.D. & Luzum, B.J., "An abridged model of the
4327		* precession-nutation of the celestial pole", Celestial Mechanics &
4328		* Dynamical Astronomy, 85, 37-49 (2003)
4329		*
4330		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4331		* IERS Technical Note No. 32, BKG (2004)
4332		*
4333		*@version 2008 May 18
4334		*
4335		* @since Release 20101201
4336		*
4337		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4338		*/
4339		public static double jauEe00b(double date1, double date2)
4340		{
4341		double ee;
4342
4343
4344		/* IAU 2000 precession-rate adjustments. */
4345	4	PrecessionDeltaTerms nutd = jauPr00(date1, date2);
4346
4347		/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
4348	4	double epsa = jauObl80(date1, date2) + nutd.depspr;
4349
4350		/* Nutation in longitude. dpsi, deps*/
4351	4	NutationTerms nut = jauNut00b(date1, date2 );
4352
4353		/* Equation of the equinoxes. */
4354	4	ee = jauEe00(date1, date2, epsa, nut.dpsi);
4355
4356	4	return ee;
4357
4358		}
4359
4360		/**
4361		* Equation of the equinoxes, compatible with IAU 2000 resolutions and
4362		* IAU 2006/2000A precession-nutation.
4363		*
4364		*<p>This function is derived from the International Astronomical Union's
4365		* SOFA (Standards Of Fundamental Astronomy) software collection.
4366		*
4367		*<p>Status: support function.
4368		*
4369		*<!-- Given: -->
4370		* @param date1 double TT as a 2-part Julian Date (Note 1)
4371		* @param date2 double TT as a 2-part Julian Date (Note 1)
4372		*
4373		* <!-- Returned (function value): -->
4374		* @return double equation of the equinoxes (Note 2)
4375		*
4376		* <p>Notes:
4377		* <ol>
4378		*
4379		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
4380		* convenient way between the two arguments. For example,
4381		* JD(TT)=2450123.7 could be expressed in any of these ways,
4382		* among others:
4383		*<pre>
4384		* date1 date2
4385		*
4386		* 2450123.7 0.0 (JD method)
4387		* 2451545.0 -1421.3 (J2000 method)
4388		* 2400000.5 50123.2 (MJD method)
4389		* 2450123.5 0.2 (date & time method)
4390		*</pre>
4391		* The JD method is the most natural and convenient to use in
4392		* cases where the loss of several decimal digits of resolution
4393		* is acceptable. The J2000 method is best matched to the way
4394		* the argument is handled internally and will deliver the
4395		* optimum resolution. The MJD method and the date & time methods
4396		* are both good compromises between resolution and convenience.
4397		*
4398		* <li> The result, which is in radians, operates in the following sense:
4399		*
4400		* Greenwich apparent ST = GMST + equation of the equinoxes
4401		*</ol>
4402		*<p>Called:<ul>
4403		* <li>{@link #jauAnpm} normalize angle into range +/- pi
4404		* <li>{@link #jauGst06a} Greenwich apparent sidereal time, IAU 2006/2000A
4405		* <li>{@link #jauGmst06} Greenwich mean sidereal time, IAU 2006
4406		* </ul>
4407		*<p>Reference:
4408		*
4409		* <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
4410		* IERS Technical Note No. 32, BKG
4411		*
4412		*@version 2008 May 18
4413		*
4414		* @since Release 20101201
4415		*
4416		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4417		*/
4418		public static double jauEe06a(double date1, double date2)
4419		{
4420		double gst06a, gmst06, ee;
4421
4422
4423		/* Apparent and mean sidereal times. */
4424	2	gst06a = jauGst06a(0.0, 0.0, date1, date2);
4425	2	gmst06 = jauGmst06(0.0, 0.0, date1, date2);
4426
4427		/* Equation of the equinoxes. */
4428	2	ee = jauAnpm(gst06a - gmst06);
4429
4430	2	return ee;
4431
4432		}
4433
4434		private static class TERM {
4435		final int nfa[]; /* coefficients of l,l',F,D,Om,LVe,LE,pA */
4436		final double s, c; /* sine and cosine coefficients */
4437	4964	public TERM(int nfa[], double s, double c) {
4438	4964	this.nfa = nfa;
4439	4964	this.s = s;
4440	4964	this.c = c;
4441	4964	}
4442
4443		}
4444
4445
4446		/**
4447		* Equation of the equinoxes complementary terms, consistent with
4448		* IAU 2000 resolutions.
4449		*
4450		*<p>This function is derived from the International Astronomical Union's
4451		* SOFA (Standards Of Fundamental Astronomy) software collection.
4452		*
4453		*<p>Status: canonical model.
4454		*
4455		*<!-- Given: -->
4456		* @param date1 double TT as a 2-part Julian Date (Note 1)
4457		* @param date2 double TT as a 2-part Julian Date (Note 1)
4458		*
4459		* <!-- Returned (function value): -->
4460		* @return double complementary terms (Note 2)
4461		*
4462		* <p>Notes:
4463		* <ol>
4464		*
4465		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
4466		* convenient way between the two arguments. For example,
4467		* JD(TT)=2450123.7 could be expressed in any of these ways,
4468		* among others:
4469		*<pre>
4470		* date1 date2
4471		*
4472		* 2450123.7 0.0 (JD method)
4473		* 2451545.0 -1421.3 (J2000 method)
4474		* 2400000.5 50123.2 (MJD method)
4475		* 2450123.5 0.2 (date & time method)
4476		*</pre>
4477		* The JD method is the most natural and convenient to use in
4478		* cases where the loss of several decimal digits of resolution
4479		* is acceptable. The J2000 method is best matched to the way
4480		* the argument is handled internally and will deliver the
4481		* optimum resolution. The MJD method and the date & time methods
4482		* are both good compromises between resolution and convenience.
4483		*
4484		* <li> The "complementary terms" are part of the equation of the
4485		* equinoxes (EE), classically the difference between apparent and
4486		* mean Sidereal Time:
4487		*
4488		* GAST = GMST + EE
4489		*
4490		* with:
4491		*
4492		* EE = dpsi * cos(eps)
4493		*
4494		* where dpsi is the nutation in longitude and eps is the obliquity
4495		* of date. However, if the rotation of the Earth were constant in
4496		* an inertial frame the classical formulation would lead to
4497		* apparent irregularities in the UT1 timescale traceable to side-
4498		* effects of precession-nutation. In order to eliminate these
4499		* effects from UT1, "complementary terms" were introduced in 1994
4500		* (IAU, 1994) and took effect from 1997 (Capitaine and Gontier,
4501		* <li>:
4502		*
4503		* GAST = GMST + CT + EE
4504		*
4505		* By convention, the complementary terms are included as part of
4506		* the equation of the equinoxes rather than as part of the mean
4507		* Sidereal Time. This slightly compromises the "geometrical"
4508		* interpretation of mean sidereal time but is otherwise
4509		* inconsequential.
4510		*
4511		* The present function computes CT in the above expression,
4512		* compatible with IAU 2000 resolutions (Capitaine et al., 2002, and
4513		* IERS Conventions 2003).
4514		*</ol>
4515		*<p>Called:<ul>
4516		* <li>{@link #jauFal03} mean anomaly of the Moon
4517		* <li>{@link #jauFalp03} mean anomaly of the Sun
4518		* <li>{@link #jauFaf03} mean argument of the latitude of the Moon
4519		* <li>{@link #jauFad03} mean elongation of the Moon from the Sun
4520		* <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
4521		* <li>{@link #jauFave03} mean longitude of Venus
4522		* <li>{@link #jauFae03} mean longitude of Earth
4523		* <li>{@link #jauFapa03} general accumulated precession in longitude
4524		* </ul>
4525		*<p>References:
4526		*
4527		* <p>Capitaine, N. & Gontier, A.-M., Astron. Astrophys., 275,
4528		* 645-650 (1993)
4529		*
4530		* <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
4531		* implement the IAU 2000 definition of UT1", Astronomy &
4532		* Astrophysics, 406, 1135-1149 (2003)
4533		*
4534		* <p>IAU Resolution C7, Recommendation 3 (1994)
4535		*
4536		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
4537		* IERS Technical Note No. 32, BKG (2004)
4538		*
4539		*@version 2009 December 17
4540		*
4541		* @since Release 20101201
4542		*
4543		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4544		*/
4545		public static double jauEect00(double date1, double date2)
4546		{
4547		/* Time since J2000.0, in Julian centuries */
4548		double t;
4549
4550		/* Miscellaneous */
4551		int i, j;
4552		double a, s0, s1;
4553
4554		/* Fundamental arguments */
4555	14	double fa[] = new double[14];
4556
4557		/* Returned value. */
4558		double eect;
4559
4560		/* ----------------------------------------- */
4561		/* The series for the EE complementary terms */
4562		/* ----------------------------------------- */
4563
4564
4565		/* Terms of order t^0 */
4566	14	final TERM e0[] = {
4567
4568		/* 1-10 */
4569		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 2640.96e-6, -0.39e-6 ),
4570		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, 63.52e-6, -0.02e-6 ),
4571		new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, 11.75e-6, 0.01e-6 ),
4572		new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, 11.21e-6, 0.01e-6 ),
4573		new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, -4.55e-6, 0.00e-6 ),
4574		new TERM(new int[]{ 0, 0, 2, 0, 3, 0, 0, 0}, 2.02e-6, 0.00e-6 ),
4575		new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.98e-6, 0.00e-6 ),
4576		new TERM(new int[]{ 0, 0, 0, 0, 3, 0, 0, 0}, -1.72e-6, 0.00e-6 ),
4577		new TERM(new int[]{ 0, 1, 0, 0, 1, 0, 0, 0}, -1.41e-6, -0.01e-6 ),
4578		new TERM(new int[]{ 0, 1, 0, 0, -1, 0, 0, 0}, -1.26e-6, -0.01e-6 ),
4579
4580		/* 11-20 */
4581		new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.63e-6, 0.00e-6 ),
4582		new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.63e-6, 0.00e-6 ),
4583		new TERM(new int[]{ 0, 1, 2, -2, 3, 0, 0, 0}, 0.46e-6, 0.00e-6 ),
4584		new TERM(new int[]{ 0, 1, 2, -2, 1, 0, 0, 0}, 0.45e-6, 0.00e-6 ),
4585		new TERM(new int[]{ 0, 0, 4, -4, 4, 0, 0, 0}, 0.36e-6, 0.00e-6 ),
4586		new TERM(new int[]{ 0, 0, 1, -1, 1, -8, 12, 0}, -0.24e-6, -0.12e-6 ),
4587		new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, 0.32e-6, 0.00e-6 ),
4588		new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, 0.28e-6, 0.00e-6 ),
4589		new TERM(new int[]{ 1, 0, 2, 0, 3, 0, 0, 0}, 0.27e-6, 0.00e-6 ),
4590		new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.26e-6, 0.00e-6 ),
4591
4592		/* 21-30 */
4593		new TERM(new int[]{ 0, 0, 2, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 ),
4594		new TERM(new int[]{ 0, 1, -2, 2, -3, 0, 0, 0}, 0.19e-6, 0.00e-6 ),
4595		new TERM(new int[]{ 0, 1, -2, 2, -1, 0, 0, 0}, 0.18e-6, 0.00e-6 ),
4596		new TERM(new int[]{ 0, 0, 0, 0, 0, 8,-13, -1}, -0.10e-6, 0.05e-6 ),
4597		new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, 0.15e-6, 0.00e-6 ),
4598		new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
4599		new TERM(new int[]{ 1, 0, 0, -2, 1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
4600		new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
4601		new TERM(new int[]{ 1, 0, 0, -2, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
4602		new TERM(new int[]{ 0, 0, 4, -2, 4, 0, 0, 0}, 0.13e-6, 0.00e-6 ),
4603
4604		/* 31-33 */
4605		new TERM(new int[]{ 0, 0, 2, -2, 4, 0, 0, 0}, -0.11e-6, 0.00e-6 ),
4606		new TERM(new int[]{ 1, 0, -2, 0, -3, 0, 0, 0}, 0.11e-6, 0.00e-6 ),
4607		new TERM(new int[]{ 1, 0, -2, 0, -1, 0, 0, 0}, 0.11e-6, 0.00e-6 )
4608		};
4609
4610		/* Terms of order t^1 */
4611	14	final TERM e1[] = {
4612		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.87e-6, 0.00e-6 )
4613		};
4614
4615		/* Number of terms in the series */
4616	14	final int NE0 = e0.length;
4617	14	final int NE1 = e1.length;
4618
4619		/--------------------------------------------------------------------/
4620
4621		/* Interval between fundamental epoch J2000.0 and current date (JC). */
4622	14	t = ((date1 - DJ00) + date2) / DJC;
4623
4624		/* Fundamental Arguments (from IERS Conventions 2003) */
4625
4626		/* Mean anomaly of the Moon. */
4627	14	fa[0] = jauFal03(t);
4628
4629		/* Mean anomaly of the Sun. */
4630	14	fa[1] = jauFalp03(t);
4631
4632		/* Mean longitude of the Moon minus that of the ascending node. */
4633	14	fa[2] = jauFaf03(t);
4634
4635		/* Mean elongation of the Moon from the Sun. */
4636	14	fa[3] = jauFad03(t);
4637
4638		/* Mean longitude of the ascending node of the Moon. */
4639	14	fa[4] = jauFaom03(t);
4640
4641		/* Mean longitude of Venus. */
4642	14	fa[5] = jauFave03(t);
4643
4644		/* Mean longitude of Earth. */
4645	14	fa[6] = jauFae03(t);
4646
4647		/* General precession in longitude. */
4648	14	fa[7] = jauFapa03(t);
4649
4650		/* Evaluate the EE complementary terms. */
4651	14	s0 = 0.0;
4652	14	s1 = 0.0;
4653
4654	476	for (i = NE0-1; i >= 0; i--) {
4655	462	a = 0.0;
4656	4158	for (j = 0; j < 8; j++) {
4657	3696	a += (double)(e0[i].nfa[j]) * fa[j];
4658		}
4659	462	s0 += e0[i].s * sin(a) + e0[i].c * cos(a);
4660		}
4661
4662	28	for (i = NE1-1; i >= 0; i--) {
4663	14	a = 0.0;
4664	126	for (j = 0; j < 8; j++) {
4665	112	a += (double)(e1[i].nfa[j]) * fa[j];
4666		}
4667	14	s1 += e1[i].s * sin(a) + e1[i].c * cos(a);
4668		}
4669
4670	14	eect = (s0 + s1 * t ) * DAS2R;
4671
4672	14	return eect;
4673
4674		}
4675
4676		/**
4677		* Reference Ellipsoid of Earth.
4678		*
4679		* The ellipsoid parameters are returned in the form of equatorial
4680		* radius in meters (a) and flattening (f). The latter is a number
4681		* around 0.00335, i.e. around 1/298.
4682		*
4683		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
4684		*
4685		* @since AIDA Stage 1
4686		*/
4687		public static class ReferenceEllipsoid{
4688		/** equatorial radius (meters, Note 2) */
4689		public double a;
4690		/** flattening (Note 2) */
4691		public double f ;
4692	48	public ReferenceEllipsoid(double a, double f ) {
4693	48	this.a = a;
4694	48	this.f = f;
4695	48	}
4696		}
4697		/**
4698		* Earth reference ellipsoids.
4699		*
4700		*<p>This function is derived from the International Astronomical Union's
4701		* JSOFA (Standards of Fundamental Astronomy) software collection.
4702		*
4703		*<p>Status: canonical.
4704		*
4705		*<!-- Given: -->
4706		* @param n int ellipsoid identifier (Note 1)
4707		*
4708		*<!-- Returned: -->
4709		* @return a double <u>returned</u> equatorial radius (meters, Note 2)
4710		* f double <u>returned</u> flattening (Note 2)
4711		*
4712		* <!-- Returned (function value): -->
4713		* @throws JSOFAIllegalParameter
4714		* int status:
4715		* 0 = OK
4716		* -1 = illegal identifier (Note 3)
4717		*
4718		* <p>Notes:
4719		* <ol>
4720		*
4721		* <li> The identifier n is a number that specifies the choice of
4722		* reference ellipsoid. The following are supported:
4723		*
4724		* n ellipsoid
4725		*
4726		* 1 WGS84
4727		* 2 GRS80
4728		* 3 WGS72
4729		*
4730		* The number n has no significance outside the JSOFA software.
4731		*
4732		* <li> The ellipsoid parameters are returned in the form of equatorial
4733		* radius in meters (a) and flattening (f). The latter is a number
4734		* around 0.00335, i.e. around 1/298.
4735		*
4736		* <li> For the case where an unsupported n value is supplied, zero a and
4737		* f are returned, as well as error status.
4738		*</ol>
4739		*<p>References:
4740		*
4741		* <p>Department of Defense World Geodetic System 1984, National
4742		* Imagery and Mapping Agency Technical Report 8350.2, Third
4743		* Edition, p3-2.
4744		*
4745		* <p>Moritz, H., Bull. Geodesique 66-2, 187 (1992).
4746		*
4747		* <p>The Department of Defense World Geodetic System 1972, World
4748		* Geodetic System Committee, May 1974.
4749		*
4750		* <p>Explanatory Supplement to the Astronomical Almanac,
4751		* P. Kenneth Seidelmann (ed), University Science Books (1992),
4752		* p220.
4753		*
4754		*@version 2010 January 18
4755		*
4756		* @since Release 20101201
4757		*
4758		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4759		*/
4760		public static ReferenceEllipsoid jauEform ( int n ) throws JSOFAIllegalParameter
4761		{
4762		double a,f;
4763		/* Look up a and f for the specified reference ellipsoid. */
4764	60	switch ( n ) {
4765		case 1:
4766
4767		/* WGS84. */
4768	36	a = 6378137.0;
4769	36	f = 1.0 / 298.257223563;
4770	36	break;
4771
4772		case 2:
4773
4774		/* GRS80. */
4775	6	a = 6378137.0;
4776	6	f = 1.0 / 298.257222101;
4777	6	break;
4778
4779		case 3:
4780
4781		/* WGS72. */
4782	6	a = 6378135.0;
4783	6	f = 1.0 / 298.26;
4784	6	break;
4785
4786		default:
4787
4788		/* Invalid identifier. */
4789	12	a = 0.0;
4790	12	f = 0.0;
4791	12	throw new JSOFAIllegalParameter("illegal ellipsoid identifier", -1);
4792
4793		}
4794
4795		/* OK status. */
4796	48	return new ReferenceEllipsoid(a, f);
4797
4798
4799		}
4800
4801
4802		/**
4803		* Equation of the origins, IAU 2006 precession and IAU 2000A nutation.
4804		*
4805		*<p>This function is derived from the International Astronomical Union's
4806		* SOFA (Standards Of Fundamental Astronomy) software collection.
4807		*
4808		*<p>Status: support function.
4809		*
4810		*<!-- Given: -->
4811		* @param date1 double TT as a 2-part Julian Date (Note 1)
4812		* @param date2 double TT as a 2-part Julian Date (Note 1)
4813		*
4814		* <!-- Returned (function value): -->
4815		* @return double equation of the origins in radians
4816		*
4817		* <p>Notes:
4818		* <ol>
4819		*
4820		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
4821		* convenient way between the two arguments. For example,
4822		* JD(TT)=2450123.7 could be expressed in any of these ways,
4823		* among others:
4824		*<pre>
4825		* date1 date2
4826		*
4827		* 2450123.7 0.0 (JD method)
4828		* 2451545.0 -1421.3 (J2000 method)
4829		* 2400000.5 50123.2 (MJD method)
4830		* 2450123.5 0.2 (date & time method)
4831		*</pre>
4832		* The JD method is the most natural and convenient to use in
4833		* cases where the loss of several decimal digits of resolution
4834		* is acceptable. The J2000 method is best matched to the way
4835		* the argument is handled internally and will deliver the
4836		* optimum resolution. The MJD method and the date & time methods
4837		* are both good compromises between resolution and convenience.
4838		*
4839		* <li> The equation of the origins is the distance between the true
4840		* equinox and the celestial intermediate origin and, equivalently,
4841		* the difference between Earth rotation angle and Greenwich
4842		* apparent sidereal time (ERA-GST). It comprises the precession
4843		* (since J2000.0) in right ascension plus the equation of the
4844		* equinoxes (including the small correction terms).
4845		*</ol>
4846		*<p>Called:<ul>
4847		* <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
4848		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
4849		* <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
4850		* <li>{@link #jauEors} equation of the origins, Given NPB matrix and s
4851		* </ul>
4852		*<p>References:
4853		*
4854		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
4855		*
4856		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
4857		*
4858		*@version 2008 May 16
4859		*
4860		* @since Release 20101201
4861		*
4862		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4863		*/
4864		public static double jauEo06a(double date1, double date2)
4865		{
4866		double r[][], s, eo;
4867
4868
4869		/* Classical nutation x precession x bias matrix. */
4870	2	r = jauPnm06a(date1, date2);
4871
4872		/* Extract CIP coordinates. */
4873	2	CelestialIntermediatePole cip = jauBpn2xy(r);
4874
4875		/* The CIO locator, s. */
4876	2	s = jauS06(date1, date2, cip.x, cip.y);
4877
4878		/* Solve for the EO. */
4879	2	eo = jauEors(r, s);
4880
4881	2	return eo;
4882
4883		}
4884
4885
4886		/**
4887		* Equation of the origins, given the classical NPB matrix and the
4888		* quantity s.
4889		*
4890		*<p>This function is derived from the International Astronomical Union's
4891		* SOFA (Standards Of Fundamental Astronomy) software collection.
4892		*
4893		*<p>Status: support function.
4894		*
4895		*<!-- Given: -->
4896		* @param rnpb double[3][3] classical nutation x precession x bias matrix
4897		* @param s double the quantity s (the CIO locator)
4898		*
4899		* <!-- Returned (function value): -->
4900		* @return double the equation of the origins in radians.
4901		*
4902		* <p>Notes:
4903		* <ol>
4904		*
4905		* <li> The equation of the origins is the distance between the true
4906		* equinox and the celestial intermediate origin and, equivalently,
4907		* the difference between Earth rotation angle and Greenwich
4908		* apparent sidereal time (ERA-GST). It comprises the precession
4909		* (since J2000.0) in right ascension plus the equation of the
4910		* equinoxes (including the small correction terms).
4911		*
4912		* <li> The algorithm is from Wallace & Capitaine (2006).
4913		*</ol>
4914		* References:
4915		*
4916		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
4917		*
4918		* <p>Wallace, P. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
4919		*
4920		*@version 2008 May 26
4921		*
4922		* @since Release 20101201
4923		*
4924		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4925		*/
4926		public static double jauEors(double rnpb[][], double s)
4927		{
4928		double x, ax, xs, ys, zs, p, q, eo;
4929
4930
4931		/* Evaluate Wallace & Capitaine (2006) expression (16). */
4932	36	x = rnpb[2][0];
4933	36	ax = x / (1.0 + rnpb[2][2]);
4934	36	xs = 1.0 - ax * x;
4935	36	ys = -ax * rnpb[2][1];
4936	36	zs = -x;
4937	36	p = rnpb[0][0] * xs + rnpb[0][1] * ys + rnpb[0][2] * zs;
4938	36	q = rnpb[1][0] * xs + rnpb[1][1] * ys + rnpb[1][2] * zs;
4939	36	eo = ((p != 0) \|\| (q != 0)) ? s - atan2(q, p) : s;
4940
4941	36	return eo;
4942
4943		}
4944
4945
4946		/**
4947		* Julian Date to Besselian Epoch.
4948		*
4949		*<p>This function is derived from the International Astronomical Union's
4950		* SOFA (Standards Of Fundamental Astronomy) software collection.
4951		*
4952		*<p>Status: support function.
4953		*
4954		*<!-- Given: -->
4955		* @param dj1 double Julian Date (see note)
4956		* @param dj2 double Julian Date (see note)
4957		*
4958		* <!-- Returned (function value): -->
4959		* @return double Besselian Epoch.
4960		*
4961		* Note:
4962		*
4963		* The Julian Date is supplied in two pieces, in the usual JSOFA
4964		* manner, which is designed to preserve time resolution. The
4965		* Julian Date is available as a single number by adding dj1 and
4966		* dj2. The maximum resolution is achieved if dj1 is 2451545D0
4967		* (J2000.0).
4968		*
4969		*<p>Reference:
4970		*
4971		* Lieske,J.H., 1979. Astron.Astrophys.,73,282.
4972		*
4973		*@version 2009 December 16
4974		*
4975		* @since Release 20101201
4976		*
4977		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
4978		*/
4979		public static double jauEpb(double dj1, double dj2)
4980		{
4981		/* J2000.0 minus B1900.0 (2415019.81352) in Julian days */
4982	2	final double D1900 = 36524.68648;
4983
4984	2	return 1900.0 + ((dj1 - DJ00) + (dj2 + D1900)) / DTY;
4985
4986		}
4987
4988		/**
4989		* Besselian Epoch to Julian Date.
4990		*
4991		*<p>This function is derived from the International Astronomical Union's
4992		* SOFA (Standards Of Fundamental Astronomy) software collection.
4993		*
4994		*<p>Status: support function.
4995		*
4996		*<!-- Given: -->
4997		* @param epb double Besselian Epoch (e.g. 1957.3D0)
4998		*
4999		*<!-- Returned: -->
5000		* @return MJD zero-point: always 2400000.5 Modified Julian Date
5001		*
5002		* Note:
5003		*
5004		* The Julian Date is returned in two pieces, in the usual JSOFA
5005		* manner, which is designed to preserve time resolution. The
5006		* Julian Date is available as a single number by adding djm0 and
5007		* djm.
5008		*
5009		*<p>Reference:
5010		*
5011		* <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
5012		*
5013		*@version 2008 May 24
5014		*
5015		* @since Release 20101201
5016		*
5017		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
5018		*/
5019		public static JulianDate jauEpb2jd(double epb)
5020		{
5021		double djm0, djm;
5022	2	djm0 = 2400000.5;
5023	2	djm = 15019.81352 + (epb - 1900.0) * DTY;
5024
5025	2	return new JulianDate(djm0, djm);
5026
5027		}
5028
5029
5030		/**
5031		* Julian Date to Julian Epoch.
5032		*
5033		*<p>This function is derived from the International Astronomical Union's
5034		* SOFA (Standards Of Fundamental Astronomy) software collection.
5035		*
5036		*<p>Status: support function.
5037		*
5038		*<!-- Given: -->
5039		* @param dj1 double Julian Date (see note)
5040		* @param dj2 double Julian Date (see note)
5041		*
5042		* <!-- Returned (function value): -->
5043		* @return double Julian Epoch
5044		*
5045		* Note:
5046		*
5047		* The Julian Date is supplied in two pieces, in the usual JSOFA
5048		* manner, which is designed to preserve time resolution. The
5049		* Julian Date is available as a single number by adding dj1 and
5050		* dj2. The maximum resolution is achieved if dj1 is 2451545D0
5051		* (J2000.0).
5052		*
5053		*<p>Reference:
5054		*
5055		* <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
5056		*
5057		*@version 2009 December 16
5058		*
5059		* @since Release 20101201
5060		*
5061		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
5062		*/
5063		public static double jauEpj(double dj1, double dj2)
5064		{
5065	2	return 2000.0 + ((dj1 - DJ00) + dj2) / DJY;
5066
5067		}
5068
5069
5070		/**
5071		* Julian Epoch to Julian Date.
5072		*
5073		*<p>This function is derived from the International Astronomical Union's
5074		* SOFA (Standards Of Fundamental Astronomy) software collection.
5075		*
5076		*<p>Status: support function.
5077		*
5078		*<!-- Given: -->
5079		* @param epj double Julian Epoch (e.g. 1996.8D0)
5080		*
5081		*<!-- Returned: -->
5082		* @return MJD zero-point: always 2400000.5 Modified Julian Date
5083		*
5084		* Note:
5085		*
5086		* The Julian Date is returned in two pieces, in the usual JSOFA
5087		* manner, which is designed to preserve time resolution. The
5088		* Julian Date is available as a single number by adding djm0 and
5089		* djm.
5090		*
5091		*<p>Reference:
5092		*
5093		* <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
5094		*
5095		*@version 2008 May 11
5096		*
5097		* @since Release 20101201
5098		*
5099		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
5100		*/
5101		public static JulianDate jauEpj2jd(double epj)
5102		{
5103		double djm0, djm;
5104	2	djm0 = 2400000.5;
5105	2	djm = 51544.5 + (epj - 2000.0) * 365.25;
5106
5107	2	return new JulianDate(djm0, djm);
5108
5109		}
5110
5111
5112		/*
5113		* A utility class to get round 65536 byte limit on functions in java - The static initializer is too large on its own. - So split into two classes for no real semantic reason
5114		*/
5115	0	static private final class Ephemeris extends SSB {
5116
5117
5118		/**
5119		* ----------------------
5120		* Ephemeris Coefficients
5121		* ----------------------
5122		*
5123		* The ephemeris consists of harmonic terms for predicting (i) the Sun
5124		* to Earth vector and (ii) the Solar-System-barycenter to Sun vector
5125		* respectively. The coefficients are stored in arrays which, although
5126		* 1-demensional, contain groups of three. Each triplet of
5127		* coefficients is the amplitude, phase and frequency for one term in
5128		* the model, and each array contains the number of terms called for by
5129		* the model.
5130		*
5131		* There are eighteen such arrays, named as follows:
5132		*<pre>
5133		* array model power of T component
5134		*
5135		* e0x Sun-to-Earth 0 x
5136		* e0y Sun-to-Earth 0 y
5137		* e0z Sun-to-Earth 0 z
5138		*
5139		* e1x Sun-to-Earth 1 x
5140		* e1y Sun-to-Earth 1 y
5141		* e1z Sun-to-Earth 1 z
5142		*
5143		* e2x Sun-to-Earth 2 x
5144		* e2y Sun-to-Earth 2 y
5145		* e2z Sun-to-Earth 2 z
5146		*
5147		* s0x SSB-to-Sun 0 x
5148		* s0y SSB-to-Sun 0 y
5149		* s0z SSB-to-Sun 0 z
5150		*
5151		* s1x SSB-to-Sun 1 x
5152		* s1y SSB-to-Sun 1 y
5153		* s1z SSB-to-Sun 1 z
5154		*
5155		* s2x SSB-to-Sun 2 x
5156		* s2y SSB-to-Sun 2 y
5157		* s2z SSB-to-Sun 2 z
5158		*<pre>
5159		*/
5160
5161		/* Sun-to-Earth, T^0, X */
5162	2	static final double e0x[] = {
5163		0.9998292878132e+00, 0.1753485171504e+01, 0.6283075850446e+01,
5164		0.8352579567414e-02, 0.1710344404582e+01, 0.1256615170089e+02,
5165		0.5611445335148e-02, 0.0000000000000e+00, 0.0000000000000e+00,
5166		0.1046664295572e-03, 0.1667225416770e+01, 0.1884922755134e+02,
5167		0.3110842534677e-04, 0.6687513390251e+00, 0.8399684731857e+02,
5168		0.2552413503550e-04, 0.5830637358413e+00, 0.5296909721118e+00,
5169		0.2137207845781e-04, 0.1092330954011e+01, 0.1577343543434e+01,
5170		0.1680240182951e-04, 0.4955366134987e+00, 0.6279552690824e+01,
5171		0.1679012370795e-04, 0.6153014091901e+01, 0.6286599010068e+01,
5172		0.1445526946777e-04, 0.3472744100492e+01, 0.2352866153506e+01,
5173
5174		0.1091038246184e-04, 0.3689845786119e+01, 0.5223693906222e+01,
5175		0.9344399733932e-05, 0.6073934645672e+01, 0.1203646072878e+02,
5176		0.8993182910652e-05, 0.3175705249069e+01, 0.1021328554739e+02,
5177		0.5665546034116e-05, 0.2152484672246e+01, 0.1059381944224e+01,
5178		0.6844146703035e-05, 0.1306964099750e+01, 0.5753384878334e+01,
5179		0.7346610905565e-05, 0.4354980070466e+01, 0.3981490189893e+00,
5180		0.6815396474414e-05, 0.2218229211267e+01, 0.4705732307012e+01,
5181		0.6112787253053e-05, 0.5384788425458e+01, 0.6812766822558e+01,
5182		0.4518120711239e-05, 0.6087604012291e+01, 0.5884926831456e+01,
5183		0.4521963430706e-05, 0.1279424524906e+01, 0.6256777527156e+01,
5184
5185		0.4497426764085e-05, 0.5369129144266e+01, 0.6309374173736e+01,
5186		0.4062190566959e-05, 0.5436473303367e+00, 0.6681224869435e+01,
5187		0.5412193480192e-05, 0.7867838528395e+00, 0.7755226100720e+00,
5188		0.5469839049386e-05, 0.1461440311134e+01, 0.1414349524433e+02,
5189		0.5205264083477e-05, 0.4432944696116e+01, 0.7860419393880e+01,
5190		0.2149759935455e-05, 0.4502237496846e+01, 0.1150676975667e+02,
5191		0.2279109618501e-05, 0.1239441308815e+01, 0.7058598460518e+01,
5192		0.2259282939683e-05, 0.3272430985331e+01, 0.4694002934110e+01,
5193		0.2558950271319e-05, 0.2265471086404e+01, 0.1216800268190e+02,
5194		0.2561581447555e-05, 0.1454740653245e+01, 0.7099330490126e+00,
5195
5196		0.1781441115440e-05, 0.2962068630206e+01, 0.7962980379786e+00,
5197		0.1612005874644e-05, 0.1473255041006e+01, 0.5486777812467e+01,
5198		0.1818630667105e-05, 0.3743903293447e+00, 0.6283008715021e+01,
5199		0.1818601377529e-05, 0.6274174354554e+01, 0.6283142985870e+01,
5200		0.1554475925257e-05, 0.1624110906816e+01, 0.2513230340178e+02,
5201		0.2090948029241e-05, 0.5852052276256e+01, 0.1179062909082e+02,
5202		0.2000176345460e-05, 0.4072093298513e+01, 0.1778984560711e+02,
5203		0.1289535917759e-05, 0.5217019331069e+01, 0.7079373888424e+01,
5204		0.1281135307881e-05, 0.4802054538934e+01, 0.3738761453707e+01,
5205		0.1518229005692e-05, 0.8691914742502e+00, 0.2132990797783e+00,
5206
5207		0.9450128579027e-06, 0.4601859529950e+01, 0.1097707878456e+02,
5208		0.7781119494996e-06, 0.1844352816694e+01, 0.8827390247185e+01,
5209		0.7733407759912e-06, 0.3582790154750e+01, 0.5507553240374e+01,
5210		0.7350644318120e-06, 0.2695277788230e+01, 0.1589072916335e+01,
5211		0.6535928827023e-06, 0.3651327986142e+01, 0.1176985366291e+02,
5212		0.6324624183656e-06, 0.2241302375862e+01, 0.6262300422539e+01,
5213		0.6298565300557e-06, 0.4407122406081e+01, 0.6303851278352e+01,
5214		0.8587037089179e-06, 0.3024307223119e+01, 0.1672837615881e+03,
5215		0.8299954491035e-06, 0.6192539428237e+01, 0.3340612434717e+01,
5216		0.6311263503401e-06, 0.2014758795416e+01, 0.7113454667900e-02,
5217
5218		0.6005646745452e-06, 0.3399500503397e+01, 0.4136910472696e+01,
5219		0.7917715109929e-06, 0.2493386877837e+01, 0.6069776770667e+01,
5220		0.7556958099685e-06, 0.4159491740143e+01, 0.6496374930224e+01,
5221		0.6773228244949e-06, 0.4034162934230e+01, 0.9437762937313e+01,
5222		0.5370708577847e-06, 0.1562219163734e+01, 0.1194447056968e+01,
5223		0.5710804266203e-06, 0.2662730803386e+01, 0.6282095334605e+01,
5224		0.5709824583726e-06, 0.3985828430833e+01, 0.6284056366286e+01,
5225		0.5143950896447e-06, 0.1308144688689e+01, 0.6290189305114e+01,
5226		0.5088010604546e-06, 0.5352817214804e+01, 0.6275962395778e+01,
5227		0.4960369085172e-06, 0.2644267922349e+01, 0.6127655567643e+01,
5228
5229		0.4803137891183e-06, 0.4008844192080e+01, 0.6438496133249e+01,
5230		0.5731747768225e-06, 0.3794550174597e+01, 0.3154687086868e+01,
5231		0.4735947960579e-06, 0.6107118308982e+01, 0.3128388763578e+01,
5232		0.4808348796625e-06, 0.4771458618163e+01, 0.8018209333619e+00,
5233		0.4115073743137e-06, 0.3327111335159e+01, 0.8429241228195e+01,
5234		0.5230575889287e-06, 0.5305708551694e+01, 0.1336797263425e+02,
5235		0.5133977889215e-06, 0.5784230738814e+01, 0.1235285262111e+02,
5236		0.5065815825327e-06, 0.2052064793679e+01, 0.1185621865188e+02,
5237		0.4339831593868e-06, 0.3644994195830e+01, 0.1726015463500e+02,
5238		0.3952928638953e-06, 0.4930376436758e+01, 0.5481254917084e+01,
5239
5240		0.4898498111942e-06, 0.4542084219731e+00, 0.9225539266174e+01,
5241		0.4757490209328e-06, 0.3161126388878e+01, 0.5856477690889e+01,
5242		0.4727701669749e-06, 0.6214993845446e+00, 0.2544314396739e+01,
5243		0.3800966681863e-06, 0.3040132339297e+01, 0.4265981595566e+00,
5244		0.3257301077939e-06, 0.8064977360087e+00, 0.3930209696940e+01,
5245		0.3255810528674e-06, 0.1974147981034e+01, 0.2146165377750e+01,
5246		0.3252029748187e-06, 0.2845924913135e+01, 0.4164311961999e+01,
5247		0.3255505635308e-06, 0.3017900824120e+01, 0.5088628793478e+01,
5248		0.2801345211990e-06, 0.6109717793179e+01, 0.1256967486051e+02,
5249		0.3688987740970e-06, 0.2911550235289e+01, 0.1807370494127e+02,
5250
5251		0.2475153429458e-06, 0.2179146025856e+01, 0.2629832328990e-01,
5252		0.3033457749150e-06, 0.1994161050744e+01, 0.4535059491685e+01,
5253		0.2186743763110e-06, 0.5125687237936e+01, 0.1137170464392e+02,
5254		0.2764777032774e-06, 0.4822646860252e+00, 0.1256262854127e+02,
5255		0.2199028768592e-06, 0.4637633293831e+01, 0.1255903824622e+02,
5256		0.2046482824760e-06, 0.1467038733093e+01, 0.7084896783808e+01,
5257		0.2611209147507e-06, 0.3044718783485e+00, 0.7143069561767e+02,
5258		0.2286079656818e-06, 0.4764220356805e+01, 0.8031092209206e+01,
5259		0.1855071202587e-06, 0.3383637774428e+01, 0.1748016358760e+01,
5260		0.2324669506784e-06, 0.6189088449251e+01, 0.1831953657923e+02,
5261
5262		0.1709528015688e-06, 0.5874966729774e+00, 0.4933208510675e+01,
5263		0.2168156875828e-06, 0.4302994009132e+01, 0.1044738781244e+02,
5264		0.2106675556535e-06, 0.3800475419891e+01, 0.7477522907414e+01,
5265		0.1430213830465e-06, 0.1294660846502e+01, 0.2942463415728e+01,
5266		0.1388396901944e-06, 0.4594797202114e+01, 0.8635942003952e+01,
5267		0.1922258844190e-06, 0.4943044543591e+00, 0.1729818233119e+02,
5268		0.1888460058292e-06, 0.2426943912028e+01, 0.1561374759853e+03,
5269		0.1789449386107e-06, 0.1582973303499e+00, 0.1592596075957e+01,
5270		0.1360803685374e-06, 0.5197240440504e+01, 0.1309584267300e+02,
5271		0.1504038014709e-06, 0.3120360916217e+01, 0.1649636139783e+02,
5272
5273		0.1382769533389e-06, 0.6164702888205e+01, 0.7632943190217e+01,
5274		0.1438059769079e-06, 0.1437423770979e+01, 0.2042657109477e+02,
5275		0.1326303260037e-06, 0.3609688799679e+01, 0.1213955354133e+02,
5276		0.1159244950540e-06, 0.5463018167225e+01, 0.5331357529664e+01,
5277		0.1433118149136e-06, 0.6028909912097e+01, 0.7342457794669e+01,
5278		0.1234623148594e-06, 0.3109645574997e+01, 0.6279485555400e+01,
5279		0.1233949875344e-06, 0.3539359332866e+01, 0.6286666145492e+01,
5280		0.9927196061299e-07, 0.1259321569772e+01, 0.7234794171227e+01,
5281		0.1242302191316e-06, 0.1065949392609e+01, 0.1511046609763e+02,
5282		0.1098402195201e-06, 0.2192508743837e+01, 0.1098880815746e+02,
5283
5284		0.1158191395315e-06, 0.4054411278650e+01, 0.5729506548653e+01,
5285		0.9048475596241e-07, 0.5429764748518e+01, 0.9623688285163e+01,
5286		0.8889853269023e-07, 0.5046586206575e+01, 0.6148010737701e+01,
5287		0.1048694242164e-06, 0.2628858030806e+01, 0.6836645152238e+01,
5288		0.1112308378646e-06, 0.4177292719907e+01, 0.1572083878776e+02,
5289		0.8631729709901e-07, 0.1601345232557e+01, 0.6418140963190e+01,
5290		0.8527816951664e-07, 0.2463888997513e+01, 0.1471231707864e+02,
5291		0.7892139456991e-07, 0.3154022088718e+01, 0.2118763888447e+01,
5292		0.1051782905236e-06, 0.4795035816088e+01, 0.1349867339771e+01,
5293		0.1048219943164e-06, 0.2952983395230e+01, 0.5999216516294e+01,
5294
5295		0.7435760775143e-07, 0.5420547991464e+01, 0.6040347114260e+01,
5296		0.9869574106949e-07, 0.3695646753667e+01, 0.6566935184597e+01,
5297		0.9156886364226e-07, 0.3922675306609e+01, 0.5643178611111e+01,
5298		0.7006834356188e-07, 0.1233968624861e+01, 0.6525804586632e+01,
5299		0.9806170182601e-07, 0.1919542280684e+01, 0.2122839202813e+02,
5300		0.9052289673607e-07, 0.4615902724369e+01, 0.4690479774488e+01,
5301		0.7554200867893e-07, 0.1236863719072e+01, 0.1253985337760e+02,
5302		0.8215741286498e-07, 0.3286800101559e+00, 0.1097355562493e+02,
5303		0.7185178575397e-07, 0.5880942158367e+01, 0.6245048154254e+01,
5304		0.7130726476180e-07, 0.7674871987661e+00, 0.6321103546637e+01,
5305
5306		0.6650894461162e-07, 0.6987129150116e+00, 0.5327476111629e+01,
5307		0.7396888823688e-07, 0.3576824794443e+01, 0.5368044267797e+00,
5308		0.7420588884775e-07, 0.5033615245369e+01, 0.2354323048545e+02,
5309		0.6141181642908e-07, 0.9449927045673e+00, 0.1296430071988e+02,
5310		0.6373557924058e-07, 0.6206342280341e+01, 0.9517183207817e+00,
5311		0.6359474329261e-07, 0.5036079095757e+01, 0.1990745094947e+01,
5312		0.5740173582646e-07, 0.6105106371350e+01, 0.9555997388169e+00,
5313		0.7019864084602e-07, 0.7237747359018e+00, 0.5225775174439e+00,
5314		0.6398054487042e-07, 0.3976367969666e+01, 0.2407292145756e+02,
5315		0.7797092650498e-07, 0.4305423910623e+01, 0.2200391463820e+02,
5316
5317		0.6466760000900e-07, 0.3500136825200e+01, 0.5230807360890e+01,
5318		0.7529417043890e-07, 0.3514779246100e+01, 0.1842262939178e+02,
5319		0.6924571140892e-07, 0.2743457928679e+01, 0.1554202828031e+00,
5320		0.6220798650222e-07, 0.2242598118209e+01, 0.1845107853235e+02,
5321		0.5870209391853e-07, 0.2332832707527e+01, 0.6398972393349e+00,
5322		0.6263953473888e-07, 0.2191105358956e+01, 0.6277552955062e+01,
5323		0.6257781390012e-07, 0.4457559396698e+01, 0.6288598745829e+01,
5324		0.5697304945123e-07, 0.3499234761404e+01, 0.1551045220144e+01,
5325		0.6335438746791e-07, 0.6441691079251e+00, 0.5216580451554e+01,
5326		0.6377258441152e-07, 0.2252599151092e+01, 0.5650292065779e+01,
5327
5328		0.6484841818165e-07, 0.1992812417646e+01, 0.1030928125552e+00,
5329		0.4735551485250e-07, 0.3744672082942e+01, 0.1431416805965e+02,
5330		0.4628595996170e-07, 0.1334226211745e+01, 0.5535693017924e+00,
5331		0.6258152336933e-07, 0.4395836159154e+01, 0.2608790314060e+02,
5332		0.6196171366594e-07, 0.2587043007997e+01, 0.8467247584405e+02,
5333		0.6159556952126e-07, 0.4782499769128e+01, 0.2394243902548e+03,
5334		0.4987741172394e-07, 0.7312257619924e+00, 0.7771377146812e+02,
5335		0.5459280703142e-07, 0.3001376372532e+01, 0.6179983037890e+01,
5336		0.4863461189999e-07, 0.3767222128541e+01, 0.9027992316901e+02,
5337		0.5349912093158e-07, 0.3663594450273e+01, 0.6386168663001e+01,
5338
5339		0.5673725607806e-07, 0.4331187919049e+01, 0.6915859635113e+01,
5340		0.4745485060512e-07, 0.5816195745518e+01, 0.6282970628506e+01,
5341		0.4745379005326e-07, 0.8323672435672e+00, 0.6283181072386e+01,
5342		0.4049002796321e-07, 0.3785023976293e+01, 0.6254626709878e+01,
5343		0.4247084014515e-07, 0.2378220728783e+01, 0.7875671926403e+01,
5344		0.4026912363055e-07, 0.2864103423269e+01, 0.6311524991013e+01,
5345		0.4062935011774e-07, 0.2415408595975e+01, 0.3634620989887e+01,
5346		0.5347771048509e-07, 0.3343479309801e+01, 0.2515860172507e+02,
5347		0.4829494136505e-07, 0.2821742398262e+01, 0.5760498333002e+01,
5348		0.4342554404599e-07, 0.5624662458712e+01, 0.7238675589263e+01,
5349
5350		0.4021599184361e-07, 0.5557250275009e+00, 0.1101510648075e+02,
5351		0.4104900474558e-07, 0.3296691780005e+01, 0.6709674010002e+01,
5352		0.4376532905131e-07, 0.3814443999443e+01, 0.6805653367890e+01,
5353		0.3314590480650e-07, 0.3560229189250e+01, 0.1259245002418e+02,
5354		0.3232421839643e-07, 0.5185389180568e+01, 0.1066495398892e+01,
5355		0.3541176318876e-07, 0.3921381909679e+01, 0.9917696840332e+01,
5356		0.3689831242681e-07, 0.4190658955386e+01, 0.1192625446156e+02,
5357		0.3890605376774e-07, 0.5546023371097e+01, 0.7478166569050e-01,
5358		0.3038559339780e-07, 0.6231032794494e+01, 0.1256621883632e+02,
5359		0.3137083969782e-07, 0.6207063419190e+01, 0.4292330755499e+01,
5360
5361		0.4024004081854e-07, 0.1195257375713e+01, 0.1334167431096e+02,
5362		0.3300234879283e-07, 0.1804694240998e+01, 0.1057540660594e+02,
5363		0.3635399155575e-07, 0.5597811343500e+01, 0.6208294184755e+01,
5364		0.3032668691356e-07, 0.3191059366530e+01, 0.1805292951336e+02,
5365		0.2809652069058e-07, 0.4094348032570e+01, 0.3523159621801e-02,
5366		0.3696955383823e-07, 0.5219282738794e+01, 0.5966683958112e+01,
5367		0.3562894142503e-07, 0.1037247544554e+01, 0.6357857516136e+01,
5368		0.3510598524148e-07, 0.1430020816116e+01, 0.6599467742779e+01,
5369		0.3617736142953e-07, 0.3002911403677e+01, 0.6019991944201e+01,
5370		0.2624524910730e-07, 0.2437046757292e+01, 0.6702560555334e+01,
5371
5372		0.2535824204490e-07, 0.1581594689647e+01, 0.3141537925223e+02,
5373		0.3519787226257e-07, 0.5379863121521e+01, 0.2505706758577e+03,
5374		0.2578406709982e-07, 0.4904222639329e+01, 0.1673046366289e+02,
5375		0.3423887981473e-07, 0.3646448997315e+01, 0.6546159756691e+01,
5376		0.2776083886467e-07, 0.3307829300144e+01, 0.1272157198369e+02,
5377		0.3379592818379e-07, 0.1747541251125e+01, 0.1494531617769e+02,
5378		0.3050255426284e-07, 0.1784689432607e-01, 0.4732030630302e+01,
5379		0.2652378350236e-07, 0.4420055276260e+01, 0.5863591145557e+01,
5380		0.2374498173768e-07, 0.3629773929208e+01, 0.2388894113936e+01,
5381		0.2716451255140e-07, 0.3079623706780e+01, 0.1202934727411e+02,
5382
5383		0.3038583699229e-07, 0.3312487903507e+00, 0.1256608456547e+02,
5384		0.2220681228760e-07, 0.5265520401774e+01, 0.1336244973887e+02,
5385		0.3044156540912e-07, 0.4766664081250e+01, 0.2908881142201e+02,
5386		0.2731859923561e-07, 0.5069146530691e+01, 0.1391601904066e+02,
5387		0.2285603018171e-07, 0.5954935112271e+01, 0.6076890225335e+01,
5388		0.2025006454555e-07, 0.4061789589267e+01, 0.4701116388778e+01,
5389		0.2012597519804e-07, 0.2485047705241e+01, 0.6262720680387e+01,
5390		0.2003406962258e-07, 0.4163779209320e+01, 0.6303431020504e+01,
5391		0.2207863441371e-07, 0.6923839133828e+00, 0.6489261475556e+01,
5392		0.2481374305624e-07, 0.5944173595676e+01, 0.1204357418345e+02,
5393
5394		0.2130923288870e-07, 0.4641013671967e+01, 0.5746271423666e+01,
5395		0.2446370543391e-07, 0.6125796518757e+01, 0.1495633313810e+00,
5396		0.1932492759052e-07, 0.2234572324504e+00, 0.1352175143971e+02,
5397		0.2600122568049e-07, 0.4281012405440e+01, 0.4590910121555e+01,
5398		0.2431754047488e-07, 0.1429943874870e+00, 0.1162474756779e+01,
5399		0.1875902869209e-07, 0.9781803816948e+00, 0.6279194432410e+01,
5400		0.1874381139426e-07, 0.5670368130173e+01, 0.6286957268481e+01,
5401		0.2156696047173e-07, 0.2008985006833e+01, 0.1813929450232e+02,
5402		0.1965076182484e-07, 0.2566186202453e+00, 0.4686889479442e+01,
5403		0.2334816372359e-07, 0.4408121891493e+01, 0.1002183730415e+02,
5404
5405		0.1869937408802e-07, 0.5272745038656e+01, 0.2427287361862e+00,
5406		0.2436236460883e-07, 0.4407720479029e+01, 0.9514313292143e+02,
5407		0.1761365216611e-07, 0.1943892315074e+00, 0.1351787002167e+02,
5408		0.2156289480503e-07, 0.1418570924545e+01, 0.6037244212485e+01,
5409		0.2164748979255e-07, 0.4724603439430e+01, 0.2301353951334e+02,
5410		0.2222286670853e-07, 0.2400266874598e+01, 0.1266924451345e+02,
5411		0.2070901414929e-07, 0.5230348028732e+01, 0.6528907488406e+01,
5412		0.1792745177020e-07, 0.2099190328945e+01, 0.6819880277225e+01,
5413		0.1841802068445e-07, 0.3467527844848e+00, 0.6514761976723e+02,
5414		0.1578401631718e-07, 0.7098642356340e+00, 0.2077542790660e-01,
5415
5416		0.1561690152531e-07, 0.5943349620372e+01, 0.6272439236156e+01,
5417		0.1558591045463e-07, 0.7040653478980e+00, 0.6293712464735e+01,
5418		0.1737356469576e-07, 0.4487064760345e+01, 0.1765478049437e+02,
5419		0.1434755619991e-07, 0.2993391570995e+01, 0.1102062672231e+00,
5420		0.1482187806654e-07, 0.2278049198251e+01, 0.1052268489556e+01,
5421		0.1424812827089e-07, 0.1682114725827e+01, 0.1311972100268e+02,
5422		0.1380282448623e-07, 0.3262668602579e+01, 0.1017725758696e+02,
5423		0.1811481244566e-07, 0.3187771221777e+01, 0.1887552587463e+02,
5424		0.1504446185696e-07, 0.5650162308647e+01, 0.7626583626240e-01,
5425		0.1740776154137e-07, 0.5487068607507e+01, 0.1965104848470e+02,
5426
5427		0.1374339536251e-07, 0.5745688172201e+01, 0.6016468784579e+01,
5428		0.1761377477704e-07, 0.5748060203659e+01, 0.2593412433514e+02,
5429		0.1535138225795e-07, 0.6226848505790e+01, 0.9411464614024e+01,
5430		0.1788140543676e-07, 0.6189318878563e+01, 0.3301902111895e+02,
5431		0.1375002807996e-07, 0.5371812884394e+01, 0.6327837846670e+00,
5432		0.1242115758632e-07, 0.1471687569712e+01, 0.3894181736510e+01,
5433		0.1450977333938e-07, 0.4143836662127e+01, 0.1277945078067e+02,
5434		0.1297579575023e-07, 0.9003477661957e+00, 0.6549682916313e+01,
5435		0.1462667934821e-07, 0.5760505536428e+01, 0.1863592847156e+02,
5436		0.1381774374799e-07, 0.1085471729463e+01, 0.2379164476796e+01,
5437
5438		0.1682333169307e-07, 0.5409870870133e+01, 0.1620077269078e+02,
5439		0.1190812918837e-07, 0.1397205174601e+01, 0.1149965630200e+02,
5440		0.1221434762106e-07, 0.9001804809095e+00, 0.1257326515556e+02,
5441		0.1549934644860e-07, 0.4262528275544e+01, 0.1820933031200e+02,
5442		0.1252138953050e-07, 0.1411642012027e+01, 0.6993008899458e+01,
5443		0.1237078905387e-07, 0.2844472403615e+01, 0.2435678079171e+02,
5444		0.1446953389615e-07, 0.5295835522223e+01, 0.3813291813120e-01,
5445		0.1388446457170e-07, 0.4969428135497e+01, 0.2458316379602e+00,
5446		0.1019339179228e-07, 0.2491369561806e+01, 0.6112403035119e+01,
5447		0.1258880815343e-07, 0.4679426248976e+01, 0.5429879531333e+01,
5448
5449		0.1297768238261e-07, 0.1074509953328e+01, 0.1249137003520e+02,
5450		0.9913505718094e-08, 0.4735097918224e+01, 0.6247047890016e+01,
5451		0.9830453155969e-08, 0.4158649187338e+01, 0.6453748665772e+01,
5452		0.1192615865309e-07, 0.3438208613699e+01, 0.6290122169689e+01,
5453		0.9835874798277e-08, 0.1913300781229e+01, 0.6319103810876e+01,
5454		0.9639087569277e-08, 0.9487683644125e+00, 0.8273820945392e+01,
5455		0.1175716107001e-07, 0.3228141664287e+01, 0.6276029531202e+01,
5456		0.1018926508678e-07, 0.2216607854300e+01, 0.1254537627298e+02,
5457		0.9500087869225e-08, 0.2625116459733e+01, 0.1256517118505e+02,
5458		0.9664192916575e-08, 0.5860562449214e+01, 0.6259197520765e+01,
5459
5460		0.9612858712203e-08, 0.7885682917381e+00, 0.6306954180126e+01,
5461		0.1117645675413e-07, 0.3932148831189e+01, 0.1779695906178e+02,
5462		0.1158864052160e-07, 0.9995605521691e+00, 0.1778273215245e+02,
5463		0.9021043467028e-08, 0.5263769742673e+01, 0.6172869583223e+01,
5464		0.8836134773563e-08, 0.1496843220365e+01, 0.1692165728891e+01,
5465		0.1045872200691e-07, 0.7009039517214e+00, 0.2204125344462e+00,
5466		0.1211463487798e-07, 0.4041544938511e+01, 0.8257698122054e+02,
5467		0.8541990804094e-08, 0.1447586692316e+01, 0.6393282117669e+01,
5468		0.1038720703636e-07, 0.4594249718112e+00, 0.1550861511662e+02,
5469		0.1126722351445e-07, 0.3925550579036e+01, 0.2061856251104e+00,
5470
5471		0.8697373859631e-08, 0.4411341856037e+01, 0.9491756770005e+00,
5472		0.8869380028441e-08, 0.2402659724813e+01, 0.3903911373650e+01,
5473		0.9247014693258e-08, 0.1401579743423e+01, 0.6267823317922e+01,
5474		0.9205062930950e-08, 0.5245978000814e+01, 0.6298328382969e+01,
5475		0.8000745038049e-08, 0.3590803356945e+01, 0.2648454860559e+01,
5476		0.9168973650819e-08, 0.2470150501679e+01, 0.1498544001348e+03,
5477		0.1075444949238e-07, 0.1328606161230e+01, 0.3694923081589e+02,
5478		0.7817298525817e-08, 0.6162256225998e+01, 0.4804209201333e+01,
5479		0.9541469226356e-08, 0.3942568967039e+01, 0.1256713221673e+02,
5480		0.9821910122027e-08, 0.2360246287233e+00, 0.1140367694411e+02,
5481
5482		0.9897822023777e-08, 0.4619805634280e+01, 0.2280573557157e+02,
5483		0.7737289283765e-08, 0.3784727847451e+01, 0.7834121070590e+01,
5484		0.9260204034710e-08, 0.2223352487601e+01, 0.2787043132925e+01,
5485		0.7320252888486e-08, 0.1288694636874e+01, 0.6282655592598e+01,
5486		0.7319785780946e-08, 0.5359869567774e+01, 0.6283496108294e+01,
5487		0.7147219933778e-08, 0.5516616675856e+01, 0.1725663147538e+02,
5488		0.7946502829878e-08, 0.2630459984567e+01, 0.1241073141809e+02,
5489		0.9001711808932e-08, 0.2849815827227e+01, 0.6281591679874e+01,
5490		0.8994041507257e-08, 0.3795244450750e+01, 0.6284560021018e+01,
5491		0.8298582787358e-08, 0.5236413127363e+00, 0.1241658836951e+02,
5492
5493		0.8526596520710e-08, 0.4794605424426e+01, 0.1098419223922e+02,
5494		0.8209822103197e-08, 0.1578752370328e+01, 0.1096996532989e+02,
5495		0.6357049861094e-08, 0.5708926113761e+01, 0.1596186371003e+01,
5496		0.7370473179049e-08, 0.3842402530241e+01, 0.4061219149443e+01,
5497		0.7232154664726e-08, 0.3067548981535e+01, 0.1610006857377e+03,
5498		0.6328765494903e-08, 0.1313930030069e+01, 0.1193336791622e+02,
5499		0.8030064908595e-08, 0.3488500408886e+01, 0.8460828644453e+00,
5500		0.6275464259232e-08, 0.1532061626198e+01, 0.8531963191132e+00,
5501		0.7051897446325e-08, 0.3285859929993e+01, 0.5849364236221e+01,
5502		0.6161593705428e-08, 0.1477341999464e+01, 0.5573142801433e+01,
5503
5504		0.7754683957278e-08, 0.1586118663096e+01, 0.8662240327241e+01,
5505		0.5889928990701e-08, 0.1304887868803e+01, 0.1232342296471e+02,
5506		0.5705756047075e-08, 0.4555333589350e+01, 0.1258692712880e+02,
5507		0.5964178808332e-08, 0.3001762842062e+01, 0.5333900173445e+01,
5508		0.6712446027467e-08, 0.4886780007595e+01, 0.1171295538178e+02,
5509		0.5941809275464e-08, 0.4701509603824e+01, 0.9779108567966e+01,
5510		0.5466993627395e-08, 0.4588357817278e+01, 0.1884211409667e+02,
5511		0.6340512090980e-08, 0.1164543038893e+01, 0.5217580628120e+02,
5512		0.6325505710045e-08, 0.3919171259645e+01, 0.1041998632314e+02,
5513		0.6164789509685e-08, 0.2143828253542e+01, 0.6151533897323e+01,
5514
5515		0.5263330812430e-08, 0.6066564434241e+01, 0.1885275071096e+02,
5516		0.5597087780221e-08, 0.2926316429472e+01, 0.4337116142245e+00,
5517		0.5396556236817e-08, 0.3244303591505e+01, 0.6286362197481e+01,
5518		0.5396615148223e-08, 0.3404304703662e+01, 0.6279789503410e+01,
5519		0.7091832443341e-08, 0.8532377803192e+00, 0.4907302013889e+01,
5520		0.6572352589782e-08, 0.4901966774419e+01, 0.1176433076753e+02,
5521		0.5960236060795e-08, 0.1874672315797e+01, 0.1422690933580e-01,
5522		0.5125480043511e-08, 0.3735726064334e+01, 0.1245594543367e+02,
5523		0.5928241866410e-08, 0.4502033899935e+01, 0.6414617803568e+01,
5524		0.5249600357424e-08, 0.4372334799878e+01, 0.1151388321134e+02,
5525
5526		0.6059171276087e-08, 0.2581617302908e+01, 0.6062663316000e+01,
5527		0.5295235081662e-08, 0.2974811513158e+01, 0.3496032717521e+01,
5528		0.5820561875933e-08, 0.1796073748244e+00, 0.2838593341516e+00,
5529		0.4754696606440e-08, 0.1981998136973e+01, 0.3104930017775e+01,
5530		0.6385053548955e-08, 0.2559174171605e+00, 0.6133512519065e+01,
5531		0.6589828273941e-08, 0.2750967106776e+01, 0.4087944051283e+02,
5532		0.5383376567189e-08, 0.6325947523578e+00, 0.2248384854122e+02,
5533		0.5928941683538e-08, 0.1672304519067e+01, 0.1581959461667e+01,
5534		0.4816060709794e-08, 0.3512566172575e+01, 0.9388005868221e+01,
5535		0.6003381586512e-08, 0.5610932219189e+01, 0.5326786718777e+01,
5536
5537		0.5504225393105e-08, 0.4037501131256e+01, 0.6503488384892e+01,
5538		0.5353772620129e-08, 0.6122774968240e+01, 0.1735668374386e+03,
5539		0.5786253768544e-08, 0.5527984999515e+01, 0.1350651127443e+00,
5540		0.5065706702002e-08, 0.9980765573624e+00, 0.1248988586463e+02,
5541		0.5972838885276e-08, 0.6044489493203e+01, 0.2673594526851e+02,
5542		0.5323585877961e-08, 0.3924265998147e+01, 0.4171425416666e+01,
5543		0.5210772682858e-08, 0.6220111376901e+01, 0.2460261242967e+02,
5544		0.4726549040535e-08, 0.3716043206862e+01, 0.7232251527446e+01,
5545		0.6029425105059e-08, 0.8548704071116e+00, 0.3227113045244e+03,
5546		0.4481542826513e-08, 0.1426925072829e+01, 0.5547199253223e+01,
5547
5548		0.5836024505068e-08, 0.7135651752625e-01, 0.7285056171570e+02,
5549		0.4137046613272e-08, 0.5330767643283e+01, 0.1087398597200e+02,
5550		0.5171977473924e-08, 0.4494262335353e+00, 0.1884570439172e+02,
5551		0.5694429833732e-08, 0.2952369582215e+01, 0.9723862754494e+02,
5552		0.4009158925298e-08, 0.3500003416535e+01, 0.6244942932314e+01,
5553		0.4784939596873e-08, 0.6196709413181e+01, 0.2929661536378e+02,
5554		0.3983725022610e-08, 0.5103690031897e+01, 0.4274518229222e+01,
5555		0.3870535232462e-08, 0.3187569587401e+01, 0.6321208768577e+01,
5556		0.5140501213951e-08, 0.1668924357457e+01, 0.1232032006293e+02,
5557		0.3849034819355e-08, 0.4445722510309e+01, 0.1726726808967e+02,
5558
5559		0.4002383075060e-08, 0.5226224152423e+01, 0.7018952447668e+01,
5560		0.3890719543549e-08, 0.4371166550274e+01, 0.1491901785440e+02,
5561		0.4887084607881e-08, 0.5973556689693e+01, 0.1478866649112e+01,
5562		0.3739939287592e-08, 0.2089084714600e+01, 0.6922973089781e+01,
5563		0.5031925918209e-08, 0.4658371936827e+01, 0.1715706182245e+02,
5564		0.4387748764954e-08, 0.4825580552819e+01, 0.2331413144044e+03,
5565		0.4147398098865e-08, 0.3739003524998e+01, 0.1376059875786e+02,
5566		0.3719089993586e-08, 0.1148941386536e+01, 0.6297302759782e+01,
5567		0.3934238461056e-08, 0.1559893008343e+01, 0.7872148766781e+01,
5568		0.3672471375622e-08, 0.5516145383612e+01, 0.6268848941110e+01,
5569
5570		0.3768911277583e-08, 0.6116053700563e+01, 0.4157198507331e+01,
5571		0.4033388417295e-08, 0.5076821746017e+01, 0.1567108171867e+02,
5572		0.3764194617832e-08, 0.8164676232075e+00, 0.3185192151914e+01,
5573		0.4840628226284e-08, 0.1360479453671e+01, 0.1252801878276e+02,
5574		0.4949443923785e-08, 0.2725622229926e+01, 0.1617106187867e+03,
5575		0.4117393089971e-08, 0.6054459628492e+00, 0.5642198095270e+01,
5576		0.3925754020428e-08, 0.8570462135210e+00, 0.2139354194808e+02,
5577		0.3630551757923e-08, 0.3552067338279e+01, 0.6294805223347e+01,
5578		0.3627274802357e-08, 0.3096565085313e+01, 0.6271346477544e+01,
5579		0.3806143885093e-08, 0.6367751709777e+00, 0.1725304118033e+02,
5580
5581		0.4433254641565e-08, 0.4848461503937e+01, 0.7445550607224e+01,
5582		0.3712319846576e-08, 0.1331950643655e+01, 0.4194847048887e+00,
5583		0.3849847534783e-08, 0.4958368297746e+00, 0.9562891316684e+00,
5584		0.3483955430165e-08, 0.2237215515707e+01, 0.1161697602389e+02,
5585		0.3961912730982e-08, 0.3332402188575e+01, 0.2277943724828e+02,
5586		0.3419978244481e-08, 0.5785600576016e+01, 0.1362553364512e+02,
5587		0.3329417758177e-08, 0.9812676559709e-01, 0.1685848245639e+02,
5588		0.4207206893193e-08, 0.9494780468236e+00, 0.2986433403208e+02,
5589		0.3268548976410e-08, 0.1739332095686e+00, 0.5749861718712e+01,
5590		0.3321880082685e-08, 0.1423354800666e+01, 0.6279143387820e+01,
5591
5592		0.4503173010852e-08, 0.2314972675293e+00, 0.1385561574497e+01,
5593		0.4316599090954e-08, 0.1012646782616e+00, 0.4176041334900e+01,
5594		0.3283493323850e-08, 0.5233306881265e+01, 0.6287008313071e+01,
5595		0.3164033542343e-08, 0.4005597257511e+01, 0.2099539292909e+02,
5596		0.4159720956725e-08, 0.5365676242020e+01, 0.5905702259363e+01,
5597		0.3565176892217e-08, 0.4284440620612e+01, 0.3932462625300e-02,
5598		0.3514440950221e-08, 0.4270562636575e+01, 0.7335344340001e+01,
5599		0.3540596871909e-08, 0.5953553201060e+01, 0.1234573916645e+02,
5600		0.2960769905118e-08, 0.1115180417718e+01, 0.2670964694522e+02,
5601		0.2962213739684e-08, 0.3863811918186e+01, 0.6408777551755e+00,
5602
5603		0.3883556700251e-08, 0.1268617928302e+01, 0.6660449441528e+01,
5604		0.2919225516346e-08, 0.4908605223265e+01, 0.1375773836557e+01,
5605		0.3115158863370e-08, 0.3744519976885e+01, 0.3802769619140e-01,
5606		0.4099438144212e-08, 0.4173244670532e+01, 0.4480965020977e+02,
5607		0.2899531858964e-08, 0.5910601428850e+01, 0.2059724391010e+02,
5608		0.3289733429855e-08, 0.2488050078239e+01, 0.1081813534213e+02,
5609		0.3933075612875e-08, 0.1122363652883e+01, 0.3773735910827e+00,
5610		0.3021403764467e-08, 0.4951973724904e+01, 0.2982630633589e+02,
5611		0.2798598949757e-08, 0.5117057845513e+01, 0.1937891852345e+02,
5612		0.3397421302707e-08, 0.6104159180476e+01, 0.6923953605621e+01,
5613
5614		0.3720398002179e-08, 0.1184933429829e+01, 0.3066615496545e+02,
5615		0.3598484186267e-08, 0.3505282086105e+01, 0.6147450479709e+01,
5616		0.3694594027310e-08, 0.2286651088141e+01, 0.2636725487657e+01,
5617		0.2680444152969e-08, 0.1871816775482e+00, 0.6816289982179e+01,
5618		0.3497574865641e-08, 0.3143251755431e+01, 0.6418701221183e+01,
5619		0.3130274129494e-08, 0.2462167316018e+01, 0.1235996607578e+02,
5620		0.3241119069551e-08, 0.4256374004686e+01, 0.1652265972112e+02,
5621		0.2601960842061e-08, 0.4970362941425e+01, 0.1045450126711e+02,
5622		0.2690601527504e-08, 0.2372657824898e+01, 0.3163918923335e+00,
5623		0.2908688152664e-08, 0.4232652627721e+01, 0.2828699048865e+02,
5624
5625		0.3120456131875e-08, 0.3925747001137e+00, 0.2195415756911e+02,
5626		0.3148855423384e-08, 0.3093478330445e+01, 0.1172006883645e+02,
5627		0.3051044261017e-08, 0.5560948248212e+01, 0.6055599646783e+01,
5628		0.2826006876660e-08, 0.5072790310072e+01, 0.5120601093667e+01,
5629		0.3100034191711e-08, 0.4998530231096e+01, 0.1799603123222e+02,
5630		0.2398771640101e-08, 0.2561739802176e+01, 0.6255674361143e+01,
5631		0.2384002842728e-08, 0.4087420284111e+01, 0.6310477339748e+01,
5632		0.2842146517568e-08, 0.2515048217955e+01, 0.5469525544182e+01,
5633		0.2847674371340e-08, 0.5235326497443e+01, 0.1034429499989e+02,
5634		0.2903722140764e-08, 0.1088200795797e+01, 0.6510552054109e+01,
5635
5636		0.3187610710605e-08, 0.4710624424816e+01, 0.1693792562116e+03,
5637		0.3048869992813e-08, 0.2857975896445e+00, 0.8390110365991e+01,
5638		0.2860216950984e-08, 0.2241619020815e+01, 0.2243449970715e+00,
5639		0.2701117683113e-08, 0.6651573305272e-01, 0.6129297044991e+01,
5640		0.2509891590152e-08, 0.1285135324585e+01, 0.1044027435778e+02,
5641		0.2623200252223e-08, 0.2981229834530e+00, 0.6436854655901e+01,
5642		0.2622541669202e-08, 0.6122470726189e+01, 0.9380959548977e+01,
5643		0.2818435667099e-08, 0.4251087148947e+01, 0.5934151399930e+01,
5644		0.2365196797465e-08, 0.3465070460790e+01, 0.2470570524223e+02,
5645		0.2358704646143e-08, 0.5791603815350e+01, 0.8671969964381e+01,
5646
5647		0.2388299481390e-08, 0.4142483772941e+01, 0.7096626156709e+01,
5648		0.1996041217224e-08, 0.2101901889496e+01, 0.1727188400790e+02,
5649		0.2687593060336e-08, 0.1526689456959e+01, 0.7075506709219e+02,
5650		0.2618913670810e-08, 0.2397684236095e+01, 0.6632000300961e+01,
5651		0.2571523050364e-08, 0.5751929456787e+00, 0.6206810014183e+01,
5652		0.2582135006946e-08, 0.5595464352926e+01, 0.4873985990671e+02,
5653		0.2372530190361e-08, 0.5092689490655e+01, 0.1590676413561e+02,
5654		0.2357178484712e-08, 0.4444363527851e+01, 0.3097883698531e+01,
5655		0.2451590394723e-08, 0.3108251687661e+01, 0.6612329252343e+00,
5656		0.2370045949608e-08, 0.2608133861079e+01, 0.3459636466239e+02,
5657
5658		0.2268997267358e-08, 0.3639717753384e+01, 0.2844914056730e-01,
5659		0.1731432137906e-08, 0.1741898445707e+00, 0.2019909489111e+02,
5660		0.1629869741622e-08, 0.3902225646724e+01, 0.3035599730800e+02,
5661		0.2206215801974e-08, 0.4971131250731e+01, 0.6281667977667e+01,
5662		0.2205469554680e-08, 0.1677462357110e+01, 0.6284483723224e+01,
5663		0.2148792362509e-08, 0.4236259604006e+01, 0.1980482729015e+02,
5664		0.1873733657847e-08, 0.5926814998687e+01, 0.2876692439167e+02,
5665		0.2026573758959e-08, 0.4349643351962e+01, 0.2449240616245e+02,
5666		0.1807770325110e-08, 0.5700940482701e+01, 0.2045286941806e+02,
5667		0.1881174408581e-08, 0.6601286363430e+00, 0.2358125818164e+02,
5668
5669		0.1368023671690e-08, 0.2211098592752e+01, 0.2473415438279e+02,
5670		0.1720017916280e-08, 0.4942488551129e+01, 0.1679593901136e+03,
5671		0.1702427665131e-08, 0.1452233856386e+01, 0.3338575901272e+03,
5672		0.1414032510054e-08, 0.5525357721439e+01, 0.1624205518357e+03,
5673		0.1652626045364e-08, 0.4108794283624e+01, 0.8956999012000e+02,
5674		0.1642957769686e-08, 0.7344335209984e+00, 0.5267006960365e+02,
5675		0.1614952403624e-08, 0.3541213951363e+01, 0.3332657872986e+02,
5676		0.1535988291188e-08, 0.4031094072151e+01, 0.3852657435933e+02,
5677		0.1593193738177e-08, 0.4185136203609e+01, 0.2282781046519e+03,
5678		0.1074569126382e-08, 0.1720485636868e+01, 0.8397383534231e+02,
5679
5680		0.1074408214509e-08, 0.2758613420318e+01, 0.8401985929482e+02,
5681		0.9700199670465e-09, 0.4216686842097e+01, 0.7826370942180e+02,
5682		0.1258433517061e-08, 0.2575068876639e+00, 0.3115650189215e+03,
5683		0.1240303229539e-08, 0.4800844956756e+00, 0.1784300471910e+03,
5684		0.9018345948127e-09, 0.3896756361552e+00, 0.5886454391678e+02,
5685		0.1135301432805e-08, 0.3700805023550e+00, 0.7842370451713e+02,
5686		0.9215887951370e-09, 0.4364579276638e+01, 0.1014262087719e+03,
5687		0.1055401054147e-08, 0.2156564222111e+01, 0.5660027930059e+02,
5688		0.1008725979831e-08, 0.5454015785234e+01, 0.4245678405627e+02,
5689		0.7217398104321e-09, 0.1597772562175e+01, 0.2457074661053e+03,
5690
5691		0.6912033134447e-09, 0.5824090621461e+01, 0.1679936946371e+03,
5692		0.6833881523549e-09, 0.3578778482835e+01, 0.6053048899753e+02,
5693		0.4887304205142e-09, 0.3724362812423e+01, 0.9656299901946e+02,
5694		0.5173709754788e-09, 0.5422427507933e+01, 0.2442876000072e+03,
5695		0.4671353097145e-09, 0.2396106924439e+01, 0.1435713242844e+03,
5696		0.5652608439480e-09, 0.2804028838685e+01, 0.8365903305582e+02,
5697		0.5604061331253e-09, 0.1638816006247e+01, 0.8433466158131e+02,
5698		0.4712723365400e-09, 0.8979003224474e+00, 0.3164282286739e+03,
5699		0.4909967465112e-09, 0.3210426725516e+01, 0.4059982187939e+03,
5700		0.4771358267658e-09, 0.5308027211629e+01, 0.1805255418145e+03,
5701
5702		0.3943451445989e-09, 0.2195145341074e+01, 0.2568537517081e+03,
5703		0.3952109120244e-09, 0.5081189491586e+01, 0.2449975330562e+03,
5704		0.3788134594789e-09, 0.4345171264441e+01, 0.1568131045107e+03,
5705		0.3738330190479e-09, 0.2613062847997e+01, 0.3948519331910e+03,
5706		0.3099866678136e-09, 0.2846760817689e+01, 0.1547176098872e+03,
5707		0.2002962716768e-09, 0.4921360989412e+01, 0.2268582385539e+03,
5708		0.2198291338754e-09, 0.1130360117454e+00, 0.1658638954901e+03,
5709		0.1491958330784e-09, 0.4228195232278e+01, 0.2219950288015e+03,
5710		0.1475384076173e-09, 0.3005721811604e+00, 0.3052819430710e+03,
5711		0.1661626624624e-09, 0.7830125621203e+00, 0.2526661704812e+03,
5712
5713		0.9015823460025e-10, 0.3807792942715e+01, 0.4171445043968e+03 };
5714
5715		/* Sun-to-Earth, T^0, Y */
5716	2	static final double e0y[] = {
5717		0.9998921098898e+00, 0.1826583913846e+00, 0.6283075850446e+01,
5718		-0.2442700893735e-01, 0.0000000000000e+00, 0.0000000000000e+00,
5719		0.8352929742915e-02, 0.1395277998680e+00, 0.1256615170089e+02,
5720		0.1046697300177e-03, 0.9641423109763e-01, 0.1884922755134e+02,
5721		0.3110841876663e-04, 0.5381140401712e+01, 0.8399684731857e+02,
5722		0.2570269094593e-04, 0.5301016407128e+01, 0.5296909721118e+00,
5723		0.2147389623610e-04, 0.2662510869850e+01, 0.1577343543434e+01,
5724		0.1680344384050e-04, 0.5207904119704e+01, 0.6279552690824e+01,
5725		0.1679117312193e-04, 0.4582187486968e+01, 0.6286599010068e+01,
5726		0.1440512068440e-04, 0.1900688517726e+01, 0.2352866153506e+01,
5727
5728		0.1135139664999e-04, 0.5273108538556e+01, 0.5223693906222e+01,
5729		0.9345482571018e-05, 0.4503047687738e+01, 0.1203646072878e+02,
5730		0.9007418719568e-05, 0.1605621059637e+01, 0.1021328554739e+02,
5731		0.5671536712314e-05, 0.5812849070861e+00, 0.1059381944224e+01,
5732		0.7451401861666e-05, 0.2807346794836e+01, 0.3981490189893e+00,
5733		0.6393470057114e-05, 0.6029224133855e+01, 0.5753384878334e+01,
5734		0.6814275881697e-05, 0.6472990145974e+00, 0.4705732307012e+01,
5735		0.6113705628887e-05, 0.3813843419700e+01, 0.6812766822558e+01,
5736		0.4503851367273e-05, 0.4527804370996e+01, 0.5884926831456e+01,
5737		0.4522249141926e-05, 0.5991783029224e+01, 0.6256777527156e+01,
5738
5739		0.4501794307018e-05, 0.3798703844397e+01, 0.6309374173736e+01,
5740		0.5514927480180e-05, 0.3961257833388e+01, 0.5507553240374e+01,
5741		0.4062862799995e-05, 0.5256247296369e+01, 0.6681224869435e+01,
5742		0.5414900429712e-05, 0.5499032014097e+01, 0.7755226100720e+00,
5743		0.5463153987424e-05, 0.6173092454097e+01, 0.1414349524433e+02,
5744		0.5071611859329e-05, 0.2870244247651e+01, 0.7860419393880e+01,
5745		0.2195112094455e-05, 0.2952338617201e+01, 0.1150676975667e+02,
5746		0.2279139233919e-05, 0.5951775132933e+01, 0.7058598460518e+01,
5747		0.2278386100876e-05, 0.4845456398785e+01, 0.4694002934110e+01,
5748		0.2559088003308e-05, 0.6945321117311e+00, 0.1216800268190e+02,
5749
5750		0.2561079286856e-05, 0.6167224608301e+01, 0.7099330490126e+00,
5751		0.1792755796387e-05, 0.1400122509632e+01, 0.7962980379786e+00,
5752		0.1818715656502e-05, 0.4703347611830e+01, 0.6283142985870e+01,
5753		0.1818744924791e-05, 0.5086748900237e+01, 0.6283008715021e+01,
5754		0.1554518791390e-05, 0.5331008042713e-01, 0.2513230340178e+02,
5755		0.2063265737239e-05, 0.4283680484178e+01, 0.1179062909082e+02,
5756		0.1497613520041e-05, 0.6074207826073e+01, 0.5486777812467e+01,
5757		0.2000617940427e-05, 0.2501426281450e+01, 0.1778984560711e+02,
5758		0.1289731195580e-05, 0.3646340599536e+01, 0.7079373888424e+01,
5759		0.1282657998934e-05, 0.3232864804902e+01, 0.3738761453707e+01,
5760
5761		0.1528915968658e-05, 0.5581433416669e+01, 0.2132990797783e+00,
5762		0.1187304098432e-05, 0.5453576453694e+01, 0.9437762937313e+01,
5763		0.7842782928118e-06, 0.2823953922273e+00, 0.8827390247185e+01,
5764		0.7352892280868e-06, 0.1124369580175e+01, 0.1589072916335e+01,
5765		0.6570189360797e-06, 0.2089154042840e+01, 0.1176985366291e+02,
5766		0.6324967590410e-06, 0.6704855581230e+00, 0.6262300422539e+01,
5767		0.6298289872283e-06, 0.2836414855840e+01, 0.6303851278352e+01,
5768		0.6476686465855e-06, 0.4852433866467e+00, 0.7113454667900e-02,
5769		0.8587034651234e-06, 0.1453511005668e+01, 0.1672837615881e+03,
5770		0.8068948788113e-06, 0.9224087798609e+00, 0.6069776770667e+01,
5771
5772		0.8353786011661e-06, 0.4631707184895e+01, 0.3340612434717e+01,
5773		0.6009324532132e-06, 0.1829498827726e+01, 0.4136910472696e+01,
5774		0.7558158559566e-06, 0.2588596800317e+01, 0.6496374930224e+01,
5775		0.5809279504503e-06, 0.5516818853476e+00, 0.1097707878456e+02,
5776		0.5374131950254e-06, 0.6275674734960e+01, 0.1194447056968e+01,
5777		0.5711160507326e-06, 0.1091905956872e+01, 0.6282095334605e+01,
5778		0.5710183170746e-06, 0.2415001635090e+01, 0.6284056366286e+01,
5779		0.5144373590610e-06, 0.6020336443438e+01, 0.6290189305114e+01,
5780		0.5103108927267e-06, 0.3775634564605e+01, 0.6275962395778e+01,
5781		0.4960654697891e-06, 0.1073450946756e+01, 0.6127655567643e+01,
5782
5783		0.4786385689280e-06, 0.2431178012310e+01, 0.6438496133249e+01,
5784		0.6109911263665e-06, 0.5343356157914e+01, 0.3154687086868e+01,
5785		0.4839898944024e-06, 0.5830833594047e-01, 0.8018209333619e+00,
5786		0.4734822623919e-06, 0.4536080134821e+01, 0.3128388763578e+01,
5787		0.4834741473290e-06, 0.2585090489754e+00, 0.7084896783808e+01,
5788		0.5134858581156e-06, 0.4213317172603e+01, 0.1235285262111e+02,
5789		0.5064004264978e-06, 0.4814418806478e+00, 0.1185621865188e+02,
5790		0.3753476772761e-06, 0.1599953399788e+01, 0.8429241228195e+01,
5791		0.4935264014283e-06, 0.2157417556873e+01, 0.2544314396739e+01,
5792		0.3950929600897e-06, 0.3359394184254e+01, 0.5481254917084e+01,
5793
5794		0.4895849789777e-06, 0.5165704376558e+01, 0.9225539266174e+01,
5795		0.4215241688886e-06, 0.2065368800993e+01, 0.1726015463500e+02,
5796		0.3796773731132e-06, 0.1468606346612e+01, 0.4265981595566e+00,
5797		0.3114178142515e-06, 0.3615638079474e+01, 0.2146165377750e+01,
5798		0.3260664220838e-06, 0.4417134922435e+01, 0.4164311961999e+01,
5799		0.3976996123008e-06, 0.4700866883004e+01, 0.5856477690889e+01,
5800		0.2801459672924e-06, 0.4538902060922e+01, 0.1256967486051e+02,
5801		0.3638931868861e-06, 0.1334197991475e+01, 0.1807370494127e+02,
5802		0.2487013269476e-06, 0.3749275558275e+01, 0.2629832328990e-01,
5803		0.3034165481994e-06, 0.4236622030873e+00, 0.4535059491685e+01,
5804
5805		0.2676278825586e-06, 0.5970848007811e+01, 0.3930209696940e+01,
5806		0.2764903818918e-06, 0.5194636754501e+01, 0.1256262854127e+02,
5807		0.2485149930507e-06, 0.1002434207846e+01, 0.5088628793478e+01,
5808		0.2199305540941e-06, 0.3066773098403e+01, 0.1255903824622e+02,
5809		0.2571106500435e-06, 0.7588312459063e+00, 0.1336797263425e+02,
5810		0.2049751817158e-06, 0.3444977434856e+01, 0.1137170464392e+02,
5811		0.2599707296297e-06, 0.1873128542205e+01, 0.7143069561767e+02,
5812		0.1785018072217e-06, 0.5015891306615e+01, 0.1748016358760e+01,
5813		0.2324833891115e-06, 0.4618271239730e+01, 0.1831953657923e+02,
5814		0.1709711119545e-06, 0.5300003455669e+01, 0.4933208510675e+01,
5815
5816		0.2107159351716e-06, 0.2229819815115e+01, 0.7477522907414e+01,
5817		0.1750333080295e-06, 0.6161485880008e+01, 0.1044738781244e+02,
5818		0.2000598210339e-06, 0.2967357299999e+01, 0.8031092209206e+01,
5819		0.1380920248681e-06, 0.3027007923917e+01, 0.8635942003952e+01,
5820		0.1412460470299e-06, 0.6037597163798e+01, 0.2942463415728e+01,
5821		0.1888459803001e-06, 0.8561476243374e+00, 0.1561374759853e+03,
5822		0.1788370542585e-06, 0.4869736290209e+01, 0.1592596075957e+01,
5823		0.1360893296167e-06, 0.3626411886436e+01, 0.1309584267300e+02,
5824		0.1506846530160e-06, 0.1550975377427e+01, 0.1649636139783e+02,
5825		0.1800913376176e-06, 0.2075826033190e+01, 0.1729818233119e+02,
5826
5827		0.1436261390649e-06, 0.6148876420255e+01, 0.2042657109477e+02,
5828		0.1220227114151e-06, 0.4382583879906e+01, 0.7632943190217e+01,
5829		0.1337883603592e-06, 0.2036644327361e+01, 0.1213955354133e+02,
5830		0.1159326650738e-06, 0.3892276994687e+01, 0.5331357529664e+01,
5831		0.1352853128569e-06, 0.1447950649744e+01, 0.1673046366289e+02,
5832		0.1433408296083e-06, 0.4457854692961e+01, 0.7342457794669e+01,
5833		0.1234701666518e-06, 0.1538818147151e+01, 0.6279485555400e+01,
5834		0.1234027192007e-06, 0.1968523220760e+01, 0.6286666145492e+01,
5835		0.1244024091797e-06, 0.5779803499985e+01, 0.1511046609763e+02,
5836		0.1097934945516e-06, 0.6210975221388e+00, 0.1098880815746e+02,
5837
5838		0.1254611329856e-06, 0.2591963807998e+01, 0.1572083878776e+02,
5839		0.1158247286784e-06, 0.2483612812670e+01, 0.5729506548653e+01,
5840		0.9039078252960e-07, 0.3857554579796e+01, 0.9623688285163e+01,
5841		0.9108024978836e-07, 0.5826368512984e+01, 0.7234794171227e+01,
5842		0.8887068108436e-07, 0.3475694573987e+01, 0.6148010737701e+01,
5843		0.8632374035438e-07, 0.3059070488983e-01, 0.6418140963190e+01,
5844		0.7893186992967e-07, 0.1583194837728e+01, 0.2118763888447e+01,
5845		0.8297650201172e-07, 0.8519770534637e+00, 0.1471231707864e+02,
5846		0.1019759578988e-06, 0.1319598738732e+00, 0.1349867339771e+01,
5847		0.1010037696236e-06, 0.9937860115618e+00, 0.6836645152238e+01,
5848
5849		0.1047727548266e-06, 0.1382138405399e+01, 0.5999216516294e+01,
5850		0.7351993881086e-07, 0.3833397851735e+01, 0.6040347114260e+01,
5851		0.9868771092341e-07, 0.2124913814390e+01, 0.6566935184597e+01,
5852		0.7007321959390e-07, 0.5946305343763e+01, 0.6525804586632e+01,
5853		0.6861411679709e-07, 0.4574654977089e+01, 0.7238675589263e+01,
5854		0.7554519809614e-07, 0.5949232686844e+01, 0.1253985337760e+02,
5855		0.9541880448335e-07, 0.3495242990564e+01, 0.2122839202813e+02,
5856		0.7185606722155e-07, 0.4310113471661e+01, 0.6245048154254e+01,
5857		0.7131360871710e-07, 0.5480309323650e+01, 0.6321103546637e+01,
5858		0.6651142021039e-07, 0.5411097713654e+01, 0.5327476111629e+01,
5859
5860		0.8538618213667e-07, 0.1827849973951e+01, 0.1101510648075e+02,
5861		0.8634954288044e-07, 0.5443584943349e+01, 0.5643178611111e+01,
5862		0.7449415051484e-07, 0.2011535459060e+01, 0.5368044267797e+00,
5863		0.7421047599169e-07, 0.3464562529249e+01, 0.2354323048545e+02,
5864		0.6140694354424e-07, 0.5657556228815e+01, 0.1296430071988e+02,
5865		0.6353525143033e-07, 0.3463816593821e+01, 0.1990745094947e+01,
5866		0.6221964013447e-07, 0.1532259498697e+01, 0.9517183207817e+00,
5867		0.5852480257244e-07, 0.1375396598875e+01, 0.9555997388169e+00,
5868		0.6398637498911e-07, 0.2405645801972e+01, 0.2407292145756e+02,
5869		0.7039744069878e-07, 0.5397541799027e+01, 0.5225775174439e+00,
5870
5871		0.6977997694382e-07, 0.4762347105419e+01, 0.1097355562493e+02,
5872		0.7460629558396e-07, 0.2711944692164e+01, 0.2200391463820e+02,
5873		0.5376577536101e-07, 0.2352980430239e+01, 0.1431416805965e+02,
5874		0.7530607893556e-07, 0.1943940180699e+01, 0.1842262939178e+02,
5875		0.6822928971605e-07, 0.4337651846959e+01, 0.1554202828031e+00,
5876		0.6220772380094e-07, 0.6716871369278e+00, 0.1845107853235e+02,
5877		0.6586950799043e-07, 0.2229714460505e+01, 0.5216580451554e+01,
5878		0.5873800565771e-07, 0.7627013920580e+00, 0.6398972393349e+00,
5879		0.6264346929745e-07, 0.6202785478961e+00, 0.6277552955062e+01,
5880		0.6257929115669e-07, 0.2886775596668e+01, 0.6288598745829e+01,
5881
5882		0.5343536033409e-07, 0.1977241012051e+01, 0.4690479774488e+01,
5883		0.5587849781714e-07, 0.1922923484825e+01, 0.1551045220144e+01,
5884		0.6905100845603e-07, 0.3570757164631e+01, 0.1030928125552e+00,
5885		0.6178957066649e-07, 0.5197558947765e+01, 0.5230807360890e+01,
5886		0.6187270224331e-07, 0.8193497368922e+00, 0.5650292065779e+01,
5887		0.5385664291426e-07, 0.5406336665586e+01, 0.7771377146812e+02,
5888		0.6329363917926e-07, 0.2837760654536e+01, 0.2608790314060e+02,
5889		0.4546018761604e-07, 0.2933580297050e+01, 0.5535693017924e+00,
5890		0.6196091049375e-07, 0.4157871494377e+01, 0.8467247584405e+02,
5891		0.6159555108218e-07, 0.3211703561703e+01, 0.2394243902548e+03,
5892
5893		0.4995340539317e-07, 0.1459098102922e+01, 0.4732030630302e+01,
5894		0.5457031243572e-07, 0.1430457676136e+01, 0.6179983037890e+01,
5895		0.4863461418397e-07, 0.2196425916730e+01, 0.9027992316901e+02,
5896		0.5342947626870e-07, 0.2086612890268e+01, 0.6386168663001e+01,
5897		0.5674296648439e-07, 0.2760204966535e+01, 0.6915859635113e+01,
5898		0.4745783120161e-07, 0.4245368971862e+01, 0.6282970628506e+01,
5899		0.4745676961198e-07, 0.5544725787016e+01, 0.6283181072386e+01,
5900		0.4049796869973e-07, 0.2213984363586e+01, 0.6254626709878e+01,
5901		0.4248333596940e-07, 0.8075781952896e+00, 0.7875671926403e+01,
5902		0.4027178070205e-07, 0.1293268540378e+01, 0.6311524991013e+01,
5903
5904		0.4066543943476e-07, 0.3986141175804e+01, 0.3634620989887e+01,
5905		0.4858863787880e-07, 0.1276112738231e+01, 0.5760498333002e+01,
5906		0.5277398263530e-07, 0.4916111741527e+01, 0.2515860172507e+02,
5907		0.4105635656559e-07, 0.1725805864426e+01, 0.6709674010002e+01,
5908		0.4376781925772e-07, 0.2243642442106e+01, 0.6805653367890e+01,
5909		0.3235827894693e-07, 0.3614135118271e+01, 0.1066495398892e+01,
5910		0.3073244740308e-07, 0.2460873393460e+01, 0.5863591145557e+01,
5911		0.3088609271373e-07, 0.5678431771790e+01, 0.9917696840332e+01,
5912		0.3393022279836e-07, 0.3814017477291e+01, 0.1391601904066e+02,
5913		0.3038686508802e-07, 0.4660216229171e+01, 0.1256621883632e+02,
5914
5915		0.4019677752497e-07, 0.5906906243735e+01, 0.1334167431096e+02,
5916		0.3288834998232e-07, 0.9536146445882e+00, 0.1620077269078e+02,
5917		0.3889973794631e-07, 0.3942205097644e+01, 0.7478166569050e-01,
5918		0.3050438987141e-07, 0.1624810271286e+01, 0.1805292951336e+02,
5919		0.3601142564638e-07, 0.4030467142575e+01, 0.6208294184755e+01,
5920		0.3689015557141e-07, 0.3648878818694e+01, 0.5966683958112e+01,
5921		0.3563471893565e-07, 0.5749584017096e+01, 0.6357857516136e+01,
5922		0.2776183170667e-07, 0.2630124187070e+01, 0.3523159621801e-02,
5923		0.2922350530341e-07, 0.1790346403629e+01, 0.1272157198369e+02,
5924		0.3511076917302e-07, 0.6142198301611e+01, 0.6599467742779e+01,
5925
5926		0.3619351007632e-07, 0.1432421386492e+01, 0.6019991944201e+01,
5927		0.2561254711098e-07, 0.2302822475792e+01, 0.1259245002418e+02,
5928		0.2626903942920e-07, 0.8660470994571e+00, 0.6702560555334e+01,
5929		0.2550187397083e-07, 0.6069721995383e+01, 0.1057540660594e+02,
5930		0.2535873526138e-07, 0.1079020331795e-01, 0.3141537925223e+02,
5931		0.3519786153847e-07, 0.3809066902283e+01, 0.2505706758577e+03,
5932		0.3424651492873e-07, 0.2075435114417e+01, 0.6546159756691e+01,
5933		0.2372676630861e-07, 0.2057803120154e+01, 0.2388894113936e+01,
5934		0.2710980779541e-07, 0.1510068488010e+01, 0.1202934727411e+02,
5935		0.3038710889704e-07, 0.5043617528901e+01, 0.1256608456547e+02,
5936
5937		0.2220364130585e-07, 0.3694793218205e+01, 0.1336244973887e+02,
5938		0.3025880825460e-07, 0.5450618999049e-01, 0.2908881142201e+02,
5939		0.2784493486864e-07, 0.3381164084502e+01, 0.1494531617769e+02,
5940		0.2294414142438e-07, 0.4382309025210e+01, 0.6076890225335e+01,
5941		0.2012723294724e-07, 0.9142212256518e+00, 0.6262720680387e+01,
5942		0.2036357831958e-07, 0.5676172293154e+01, 0.4701116388778e+01,
5943		0.2003474823288e-07, 0.2592767977625e+01, 0.6303431020504e+01,
5944		0.2207144900109e-07, 0.5404976271180e+01, 0.6489261475556e+01,
5945		0.2481664905135e-07, 0.4373284587027e+01, 0.1204357418345e+02,
5946		0.2674949182295e-07, 0.5859182188482e+01, 0.4590910121555e+01,
5947
5948		0.2450554720322e-07, 0.4555381557451e+01, 0.1495633313810e+00,
5949		0.2601975986457e-07, 0.3933165584959e+01, 0.1965104848470e+02,
5950		0.2199860022848e-07, 0.5227977189087e+01, 0.1351787002167e+02,
5951		0.2448121172316e-07, 0.4858060353949e+01, 0.1162474756779e+01,
5952		0.1876014864049e-07, 0.5690546553605e+01, 0.6279194432410e+01,
5953		0.1874513219396e-07, 0.4099539297446e+01, 0.6286957268481e+01,
5954		0.2156380842559e-07, 0.4382594769913e+00, 0.1813929450232e+02,
5955		0.1981691240061e-07, 0.1829784152444e+01, 0.4686889479442e+01,
5956		0.2329992648539e-07, 0.2836254278973e+01, 0.1002183730415e+02,
5957		0.1765184135302e-07, 0.2803494925833e+01, 0.4292330755499e+01,
5958
5959		0.2436368366085e-07, 0.2836897959677e+01, 0.9514313292143e+02,
5960		0.2164089203889e-07, 0.6127522446024e+01, 0.6037244212485e+01,
5961		0.1847755034221e-07, 0.3683163635008e+01, 0.2427287361862e+00,
5962		0.1674798769966e-07, 0.3316993867246e+00, 0.1311972100268e+02,
5963		0.2222542124356e-07, 0.8294097805480e+00, 0.1266924451345e+02,
5964		0.2071074505925e-07, 0.3659492220261e+01, 0.6528907488406e+01,
5965		0.1608224471835e-07, 0.4774492067182e+01, 0.1352175143971e+02,
5966		0.1857583439071e-07, 0.2873120597682e+01, 0.8662240327241e+01,
5967		0.1793018836159e-07, 0.5282441177929e+00, 0.6819880277225e+01,
5968		0.1575391221692e-07, 0.1320789654258e+01, 0.1102062672231e+00,
5969
5970		0.1840132009557e-07, 0.1917110916256e+01, 0.6514761976723e+02,
5971		0.1760917288281e-07, 0.2972635937132e+01, 0.5746271423666e+01,
5972		0.1561779518516e-07, 0.4372569261981e+01, 0.6272439236156e+01,
5973		0.1558687885205e-07, 0.5416424926425e+01, 0.6293712464735e+01,
5974		0.1951359382579e-07, 0.3094448898752e+01, 0.2301353951334e+02,
5975		0.1569144275614e-07, 0.2802103689808e+01, 0.1765478049437e+02,
5976		0.1479130389462e-07, 0.2136435020467e+01, 0.2077542790660e-01,
5977		0.1467828510764e-07, 0.7072627435674e+00, 0.1052268489556e+01,
5978		0.1627627337440e-07, 0.3947607143237e+01, 0.6327837846670e+00,
5979		0.1503498479758e-07, 0.4079248909190e+01, 0.7626583626240e-01,
5980
5981		0.1297967708237e-07, 0.6269637122840e+01, 0.1149965630200e+02,
5982		0.1374416896634e-07, 0.4175657970702e+01, 0.6016468784579e+01,
5983		0.1783812325219e-07, 0.1476540547560e+01, 0.3301902111895e+02,
5984		0.1525884228756e-07, 0.4653477715241e+01, 0.9411464614024e+01,
5985		0.1451067396763e-07, 0.2573001128225e+01, 0.1277945078067e+02,
5986		0.1297713111950e-07, 0.5612799618771e+01, 0.6549682916313e+01,
5987		0.1462784012820e-07, 0.4189661623870e+01, 0.1863592847156e+02,
5988		0.1384185980007e-07, 0.2656915472196e+01, 0.2379164476796e+01,
5989		0.1221497599801e-07, 0.5612515760138e+01, 0.1257326515556e+02,
5990		0.1560574525896e-07, 0.4783414317919e+01, 0.1887552587463e+02,
5991
5992		0.1544598372036e-07, 0.2694431138063e+01, 0.1820933031200e+02,
5993		0.1531678928696e-07, 0.4105103489666e+01, 0.2593412433514e+02,
5994		0.1349321503795e-07, 0.3082437194015e+00, 0.5120601093667e+01,
5995		0.1252030290917e-07, 0.6124072334087e+01, 0.6993008899458e+01,
5996		0.1459243816687e-07, 0.3733103981697e+01, 0.3813291813120e-01,
5997		0.1226103625262e-07, 0.1267127706817e+01, 0.2435678079171e+02,
5998		0.1019449641504e-07, 0.4367790112269e+01, 0.1725663147538e+02,
5999		0.1380789433607e-07, 0.3387201768700e+01, 0.2458316379602e+00,
6000		0.1019453421658e-07, 0.9204143073737e+00, 0.6112403035119e+01,
6001		0.1297929434405e-07, 0.5786874896426e+01, 0.1249137003520e+02,
6002
6003		0.9912677786097e-08, 0.3164232870746e+01, 0.6247047890016e+01,
6004		0.9829386098599e-08, 0.2586762413351e+01, 0.6453748665772e+01,
6005		0.1226807746104e-07, 0.6239068436607e+01, 0.5429879531333e+01,
6006		0.1192691755997e-07, 0.1867380051424e+01, 0.6290122169689e+01,
6007		0.9836499227081e-08, 0.3424716293727e+00, 0.6319103810876e+01,
6008		0.9642862564285e-08, 0.5661372990657e+01, 0.8273820945392e+01,
6009		0.1165184404862e-07, 0.5768367239093e+01, 0.1778273215245e+02,
6010		0.1175794418818e-07, 0.1657351222943e+01, 0.6276029531202e+01,
6011		0.1018948635601e-07, 0.6458292350865e+00, 0.1254537627298e+02,
6012		0.9500383606676e-08, 0.1054306140741e+01, 0.1256517118505e+02,
6013
6014		0.1227512202906e-07, 0.2505278379114e+01, 0.2248384854122e+02,
6015		0.9664792009993e-08, 0.4289737277000e+01, 0.6259197520765e+01,
6016		0.9613285666331e-08, 0.5500597673141e+01, 0.6306954180126e+01,
6017		0.1117906736211e-07, 0.2361405953468e+01, 0.1779695906178e+02,
6018		0.9611378640782e-08, 0.2851310576269e+01, 0.2061856251104e+00,
6019		0.8845354852370e-08, 0.6208777705343e+01, 0.1692165728891e+01,
6020		0.1054046966600e-07, 0.5413091423934e+01, 0.2204125344462e+00,
6021		0.1215539124483e-07, 0.5613969479755e+01, 0.8257698122054e+02,
6022		0.9932460955209e-08, 0.1106124877015e+01, 0.1017725758696e+02,
6023		0.8785804715043e-08, 0.2869224476477e+01, 0.9491756770005e+00,
6024
6025		0.8538084097562e-08, 0.6159640899344e+01, 0.6393282117669e+01,
6026		0.8648994369529e-08, 0.1374901198784e+01, 0.4804209201333e+01,
6027		0.1039063219067e-07, 0.5171080641327e+01, 0.1550861511662e+02,
6028		0.8867983926439e-08, 0.8317320304902e+00, 0.3903911373650e+01,
6029		0.8327495955244e-08, 0.3605591969180e+01, 0.6172869583223e+01,
6030		0.9243088356133e-08, 0.6114299196843e+01, 0.6267823317922e+01,
6031		0.9205657357835e-08, 0.3675153683737e+01, 0.6298328382969e+01,
6032		0.1033269714606e-07, 0.3313328813024e+01, 0.5573142801433e+01,
6033		0.8001706275552e-08, 0.2019980960053e+01, 0.2648454860559e+01,
6034		0.9171858254191e-08, 0.8992015524177e+00, 0.1498544001348e+03,
6035
6036		0.1075327150242e-07, 0.2898669963648e+01, 0.3694923081589e+02,
6037		0.9884866689828e-08, 0.4946715904478e+01, 0.1140367694411e+02,
6038		0.9541835576677e-08, 0.2371787888469e+01, 0.1256713221673e+02,
6039		0.7739903376237e-08, 0.2213775190612e+01, 0.7834121070590e+01,
6040		0.7311962684106e-08, 0.3429378787739e+01, 0.1192625446156e+02,
6041		0.9724904869624e-08, 0.6195878564404e+01, 0.2280573557157e+02,
6042		0.9251628983612e-08, 0.6511509527390e+00, 0.2787043132925e+01,
6043		0.7320763787842e-08, 0.6001083639421e+01, 0.6282655592598e+01,
6044		0.7320296650962e-08, 0.3789073265087e+01, 0.6283496108294e+01,
6045		0.7947032271039e-08, 0.1059659582204e+01, 0.1241073141809e+02,
6046
6047		0.9005277053115e-08, 0.1280315624361e+01, 0.6281591679874e+01,
6048		0.8995601652048e-08, 0.2224439106766e+01, 0.6284560021018e+01,
6049		0.8288040568796e-08, 0.5234914433867e+01, 0.1241658836951e+02,
6050		0.6359381347255e-08, 0.4137989441490e+01, 0.1596186371003e+01,
6051		0.8699572228626e-08, 0.1758411009497e+01, 0.6133512519065e+01,
6052		0.6456797542736e-08, 0.5919285089994e+01, 0.1685848245639e+02,
6053		0.7424573475452e-08, 0.5414616938827e+01, 0.4061219149443e+01,
6054		0.7235671196168e-08, 0.1496516557134e+01, 0.1610006857377e+03,
6055		0.8104015182733e-08, 0.1919918242764e+01, 0.8460828644453e+00,
6056		0.8098576535937e-08, 0.3819615855458e+01, 0.3894181736510e+01,
6057
6058		0.6275292346625e-08, 0.6244264115141e+01, 0.8531963191132e+00,
6059		0.6052432989112e-08, 0.5037731872610e+00, 0.1567108171867e+02,
6060		0.5705651535817e-08, 0.2984557271995e+01, 0.1258692712880e+02,
6061		0.5789650115138e-08, 0.6087038140697e+01, 0.1193336791622e+02,
6062		0.5512132153377e-08, 0.5855668994076e+01, 0.1232342296471e+02,
6063		0.7388890819102e-08, 0.2443128574740e+01, 0.4907302013889e+01,
6064		0.5467593991798e-08, 0.3017561234194e+01, 0.1884211409667e+02,
6065		0.6388519802999e-08, 0.5887386712935e+01, 0.5217580628120e+02,
6066		0.6106777149944e-08, 0.3483461059895e+00, 0.1422690933580e-01,
6067		0.7383420275489e-08, 0.5417387056707e+01, 0.2358125818164e+02,
6068
6069		0.5505208141738e-08, 0.2848193644783e+01, 0.1151388321134e+02,
6070		0.6310757462877e-08, 0.2349882520828e+01, 0.1041998632314e+02,
6071		0.6166904929691e-08, 0.5728575944077e+00, 0.6151533897323e+01,
6072		0.5263442042754e-08, 0.4495796125937e+01, 0.1885275071096e+02,
6073		0.5591828082629e-08, 0.1355441967677e+01, 0.4337116142245e+00,
6074		0.5397051680497e-08, 0.1673422864307e+01, 0.6286362197481e+01,
6075		0.5396992745159e-08, 0.1833502206373e+01, 0.6279789503410e+01,
6076		0.6572913000726e-08, 0.3331122065824e+01, 0.1176433076753e+02,
6077		0.5123421866413e-08, 0.2165327142679e+01, 0.1245594543367e+02,
6078		0.5930495725999e-08, 0.2931146089284e+01, 0.6414617803568e+01,
6079
6080		0.6431797403933e-08, 0.4134407994088e+01, 0.1350651127443e+00,
6081		0.5003182207604e-08, 0.3805420303749e+01, 0.1096996532989e+02,
6082		0.5587731032504e-08, 0.1082469260599e+01, 0.6062663316000e+01,
6083		0.5935263407816e-08, 0.8384333678401e+00, 0.5326786718777e+01,
6084		0.4756019827760e-08, 0.3552588749309e+01, 0.3104930017775e+01,
6085		0.6599951172637e-08, 0.4320826409528e+01, 0.4087944051283e+02,
6086		0.5902606868464e-08, 0.4811879454445e+01, 0.5849364236221e+01,
6087		0.5921147809031e-08, 0.9942628922396e-01, 0.1581959461667e+01,
6088		0.5505382581266e-08, 0.2466557607764e+01, 0.6503488384892e+01,
6089		0.5353771071862e-08, 0.4551978748683e+01, 0.1735668374386e+03,
6090
6091		0.5063282210946e-08, 0.5710812312425e+01, 0.1248988586463e+02,
6092		0.5926120403383e-08, 0.1333998428358e+01, 0.2673594526851e+02,
6093		0.5211016176149e-08, 0.4649315360760e+01, 0.2460261242967e+02,
6094		0.5347075084894e-08, 0.5512754081205e+01, 0.4171425416666e+01,
6095		0.4872609773574e-08, 0.1308025299938e+01, 0.5333900173445e+01,
6096		0.4727711321420e-08, 0.2144908368062e+01, 0.7232251527446e+01,
6097		0.6029426018652e-08, 0.5567259412084e+01, 0.3227113045244e+03,
6098		0.4321485284369e-08, 0.5230667156451e+01, 0.9388005868221e+01,
6099		0.4476406760553e-08, 0.6134081115303e+01, 0.5547199253223e+01,
6100		0.5835268277420e-08, 0.4783808492071e+01, 0.7285056171570e+02,
6101
6102		0.5172183602748e-08, 0.5161817911099e+01, 0.1884570439172e+02,
6103		0.5693571465184e-08, 0.1381646203111e+01, 0.9723862754494e+02,
6104		0.4060634965349e-08, 0.3876705259495e+00, 0.4274518229222e+01,
6105		0.3967398770473e-08, 0.5029491776223e+01, 0.3496032717521e+01,
6106		0.3943754005255e-08, 0.1923162955490e+01, 0.6244942932314e+01,
6107		0.4781323427824e-08, 0.4633332586423e+01, 0.2929661536378e+02,
6108		0.3871483781204e-08, 0.1616650009743e+01, 0.6321208768577e+01,
6109		0.5141741733997e-08, 0.9817316704659e-01, 0.1232032006293e+02,
6110		0.4002385978497e-08, 0.3656161212139e+01, 0.7018952447668e+01,
6111		0.4901092604097e-08, 0.4404098713092e+01, 0.1478866649112e+01,
6112
6113		0.3740932630345e-08, 0.5181188732639e+00, 0.6922973089781e+01,
6114		0.4387283718538e-08, 0.3254859566869e+01, 0.2331413144044e+03,
6115		0.5019197802033e-08, 0.3086773224677e+01, 0.1715706182245e+02,
6116		0.3834931695175e-08, 0.2797882673542e+01, 0.1491901785440e+02,
6117		0.3760413942497e-08, 0.2892676280217e+01, 0.1726726808967e+02,
6118		0.3719717204628e-08, 0.5861046025739e+01, 0.6297302759782e+01,
6119		0.4145623530149e-08, 0.2168239627033e+01, 0.1376059875786e+02,
6120		0.3932788425380e-08, 0.6271811124181e+01, 0.7872148766781e+01,
6121		0.3686377476857e-08, 0.3936853151404e+01, 0.6268848941110e+01,
6122		0.3779077950339e-08, 0.1404148734043e+01, 0.4157198507331e+01,
6123
6124		0.4091334550598e-08, 0.2452436180854e+01, 0.9779108567966e+01,
6125		0.3926694536146e-08, 0.6102292739040e+01, 0.1098419223922e+02,
6126		0.4841000253289e-08, 0.6072760457276e+01, 0.1252801878276e+02,
6127		0.4949340130240e-08, 0.1154832815171e+01, 0.1617106187867e+03,
6128		0.3761557737360e-08, 0.5527545321897e+01, 0.3185192151914e+01,
6129		0.3647396268188e-08, 0.1525035688629e+01, 0.6271346477544e+01,
6130		0.3932405074189e-08, 0.5570681040569e+01, 0.2139354194808e+02,
6131		0.3631322501141e-08, 0.1981240601160e+01, 0.6294805223347e+01,
6132		0.4130007425139e-08, 0.2050060880201e+01, 0.2195415756911e+02,
6133		0.4433905965176e-08, 0.3277477970321e+01, 0.7445550607224e+01,
6134
6135		0.3851814176947e-08, 0.5210690074886e+01, 0.9562891316684e+00,
6136		0.3485807052785e-08, 0.6653274904611e+00, 0.1161697602389e+02,
6137		0.3979772816991e-08, 0.1767941436148e+01, 0.2277943724828e+02,
6138		0.3402607460500e-08, 0.3421746306465e+01, 0.1087398597200e+02,
6139		0.4049993000926e-08, 0.1127144787547e+01, 0.3163918923335e+00,
6140		0.3420511182382e-08, 0.4214794779161e+01, 0.1362553364512e+02,
6141		0.3640772365012e-08, 0.5324905497687e+01, 0.1725304118033e+02,
6142		0.3323037987501e-08, 0.6135761838271e+01, 0.6279143387820e+01,
6143		0.4503141663637e-08, 0.1802305450666e+01, 0.1385561574497e+01,
6144		0.4314560055588e-08, 0.4812299731574e+01, 0.4176041334900e+01,
6145
6146		0.3294226949110e-08, 0.3657547059723e+01, 0.6287008313071e+01,
6147		0.3215657197281e-08, 0.4866676894425e+01, 0.5749861718712e+01,
6148		0.4129362656266e-08, 0.3809342558906e+01, 0.5905702259363e+01,
6149		0.3137762976388e-08, 0.2494635174443e+01, 0.2099539292909e+02,
6150		0.3514010952384e-08, 0.2699961831678e+01, 0.7335344340001e+01,
6151		0.3327607571530e-08, 0.3318457714816e+01, 0.5436992986000e+01,
6152		0.3541066946675e-08, 0.4382703582466e+01, 0.1234573916645e+02,
6153		0.3216179847052e-08, 0.5271066317054e+01, 0.3802769619140e-01,
6154		0.2959045059570e-08, 0.5819591585302e+01, 0.2670964694522e+02,
6155		0.3884040326665e-08, 0.5980934960428e+01, 0.6660449441528e+01,
6156
6157		0.2922027539886e-08, 0.3337290282483e+01, 0.1375773836557e+01,
6158		0.4110846382042e-08, 0.5742978187327e+01, 0.4480965020977e+02,
6159		0.2934508411032e-08, 0.2278075804200e+01, 0.6408777551755e+00,
6160		0.3966896193000e-08, 0.5835747858477e+01, 0.3773735910827e+00,
6161		0.3286695827610e-08, 0.5838898193902e+01, 0.3932462625300e-02,
6162		0.3720643094196e-08, 0.1122212337858e+01, 0.1646033343740e+02,
6163		0.3285508906174e-08, 0.9182250996416e+00, 0.1081813534213e+02,
6164		0.3753880575973e-08, 0.5174761973266e+01, 0.5642198095270e+01,
6165		0.3022129385587e-08, 0.3381611020639e+01, 0.2982630633589e+02,
6166		0.2798569205621e-08, 0.3546193723922e+01, 0.1937891852345e+02,
6167
6168		0.3397872070505e-08, 0.4533203197934e+01, 0.6923953605621e+01,
6169		0.3708099772977e-08, 0.2756168198616e+01, 0.3066615496545e+02,
6170		0.3599283541510e-08, 0.1934395469918e+01, 0.6147450479709e+01,
6171		0.3688702753059e-08, 0.7149920971109e+00, 0.2636725487657e+01,
6172		0.2681084724003e-08, 0.4899819493154e+01, 0.6816289982179e+01,
6173		0.3495993460759e-08, 0.1572418915115e+01, 0.6418701221183e+01,
6174		0.3130770324995e-08, 0.8912190180489e+00, 0.1235996607578e+02,
6175		0.2744353821941e-08, 0.3800821940055e+01, 0.2059724391010e+02,
6176		0.2842732906341e-08, 0.2644717440029e+01, 0.2828699048865e+02,
6177		0.3046882682154e-08, 0.3987793020179e+01, 0.6055599646783e+01,
6178
6179		0.2399072455143e-08, 0.9908826440764e+00, 0.6255674361143e+01,
6180		0.2384306274204e-08, 0.2516149752220e+01, 0.6310477339748e+01,
6181		0.2977324500559e-08, 0.5849195642118e+01, 0.1652265972112e+02,
6182		0.3062835258972e-08, 0.1681660100162e+01, 0.1172006883645e+02,
6183		0.3109682589231e-08, 0.5804143987737e+00, 0.2751146787858e+02,
6184		0.2903920355299e-08, 0.5800768280123e+01, 0.6510552054109e+01,
6185		0.2823221989212e-08, 0.9241118370216e+00, 0.5469525544182e+01,
6186		0.3187949696649e-08, 0.3139776445735e+01, 0.1693792562116e+03,
6187		0.2922559771655e-08, 0.3549440782984e+01, 0.2630839062450e+00,
6188		0.2436302066603e-08, 0.4735540696319e+01, 0.3946258593675e+00,
6189
6190		0.3049473043606e-08, 0.4998289124561e+01, 0.8390110365991e+01,
6191		0.2863682575784e-08, 0.6709515671102e+00, 0.2243449970715e+00,
6192		0.2641750517966e-08, 0.5410978257284e+01, 0.2986433403208e+02,
6193		0.2704093466243e-08, 0.4778317207821e+01, 0.6129297044991e+01,
6194		0.2445522177011e-08, 0.6009020662222e+01, 0.1171295538178e+02,
6195		0.2623608810230e-08, 0.5010449777147e+01, 0.6436854655901e+01,
6196		0.2079259704053e-08, 0.5980943768809e+01, 0.2019909489111e+02,
6197		0.2820225596771e-08, 0.2679965110468e+01, 0.5934151399930e+01,
6198		0.2365221950927e-08, 0.1894231148810e+01, 0.2470570524223e+02,
6199		0.2359682077149e-08, 0.4220752950780e+01, 0.8671969964381e+01,
6200
6201		0.2387577137206e-08, 0.2571783940617e+01, 0.7096626156709e+01,
6202		0.1982102089816e-08, 0.5169765997119e+00, 0.1727188400790e+02,
6203		0.2687502389925e-08, 0.6239078264579e+01, 0.7075506709219e+02,
6204		0.2207751669135e-08, 0.2031184412677e+01, 0.4377611041777e+01,
6205		0.2618370214274e-08, 0.8266079985979e+00, 0.6632000300961e+01,
6206		0.2591951887361e-08, 0.8819350522008e+00, 0.4873985990671e+02,
6207		0.2375055656248e-08, 0.3520944177789e+01, 0.1590676413561e+02,
6208		0.2472019978911e-08, 0.1551431908671e+01, 0.6612329252343e+00,
6209		0.2368157127199e-08, 0.4178610147412e+01, 0.3459636466239e+02,
6210		0.1764846605693e-08, 0.1506764000157e+01, 0.1980094587212e+02,
6211
6212		0.2291769608798e-08, 0.2118250611782e+01, 0.2844914056730e-01,
6213		0.2209997316943e-08, 0.3363255261678e+01, 0.2666070658668e+00,
6214		0.2292699097923e-08, 0.4200423956460e+00, 0.1484170571900e-02,
6215		0.1629683015329e-08, 0.2331362582487e+01, 0.3035599730800e+02,
6216		0.2206492862426e-08, 0.3400274026992e+01, 0.6281667977667e+01,
6217		0.2205746568257e-08, 0.1066051230724e+00, 0.6284483723224e+01,
6218		0.2026310767991e-08, 0.2779066487979e+01, 0.2449240616245e+02,
6219		0.1762977622163e-08, 0.9951450691840e+00, 0.2045286941806e+02,
6220		0.1368535049606e-08, 0.6402447365817e+00, 0.2473415438279e+02,
6221		0.1720598775450e-08, 0.2303524214705e+00, 0.1679593901136e+03,
6222
6223		0.1702429015449e-08, 0.6164622655048e+01, 0.3338575901272e+03,
6224		0.1414033197685e-08, 0.3954561185580e+01, 0.1624205518357e+03,
6225		0.1573768958043e-08, 0.2028286308984e+01, 0.3144167757552e+02,
6226		0.1650705184447e-08, 0.2304040666128e+01, 0.5267006960365e+02,
6227		0.1651087618855e-08, 0.2538461057280e+01, 0.8956999012000e+02,
6228		0.1616409518983e-08, 0.5111054348152e+01, 0.3332657872986e+02,
6229		0.1537175173581e-08, 0.5601130666603e+01, 0.3852657435933e+02,
6230		0.1593191980553e-08, 0.2614340453411e+01, 0.2282781046519e+03,
6231		0.1499480170643e-08, 0.3624721577264e+01, 0.2823723341956e+02,
6232		0.1493807843235e-08, 0.4214569879008e+01, 0.2876692439167e+02,
6233
6234		0.1074571199328e-08, 0.1496911744704e+00, 0.8397383534231e+02,
6235		0.1074406983417e-08, 0.1187817671922e+01, 0.8401985929482e+02,
6236		0.9757576855851e-09, 0.2655703035858e+01, 0.7826370942180e+02,
6237		0.1258432887565e-08, 0.4969896184844e+01, 0.3115650189215e+03,
6238		0.1240336343282e-08, 0.5192460776926e+01, 0.1784300471910e+03,
6239		0.9016107005164e-09, 0.1960356923057e+01, 0.5886454391678e+02,
6240		0.1135392360918e-08, 0.5082427809068e+01, 0.7842370451713e+02,
6241		0.9216046089565e-09, 0.2793775037273e+01, 0.1014262087719e+03,
6242		0.1061276615030e-08, 0.3726144311409e+01, 0.5660027930059e+02,
6243		0.1010110596263e-08, 0.7404080708937e+00, 0.4245678405627e+02,
6244
6245		0.7217424756199e-09, 0.2697449980577e-01, 0.2457074661053e+03,
6246		0.6912003846756e-09, 0.4253296276335e+01, 0.1679936946371e+03,
6247		0.6871814664847e-09, 0.5148072412354e+01, 0.6053048899753e+02,
6248		0.4887158016343e-09, 0.2153581148294e+01, 0.9656299901946e+02,
6249		0.5161802866314e-09, 0.3852750634351e+01, 0.2442876000072e+03,
6250		0.5652599559057e-09, 0.1233233356270e+01, 0.8365903305582e+02,
6251		0.4710812608586e-09, 0.5610486976767e+01, 0.3164282286739e+03,
6252		0.4909977500324e-09, 0.1639629524123e+01, 0.4059982187939e+03,
6253		0.4772641839378e-09, 0.3737100368583e+01, 0.1805255418145e+03,
6254		0.4487562567153e-09, 0.1158417054478e+00, 0.8433466158131e+02,
6255
6256		0.3943441230497e-09, 0.6243502862796e+00, 0.2568537517081e+03,
6257		0.3952236913598e-09, 0.3510377382385e+01, 0.2449975330562e+03,
6258		0.3788898363417e-09, 0.5916128302299e+01, 0.1568131045107e+03,
6259		0.3738329328831e-09, 0.1042266763456e+01, 0.3948519331910e+03,
6260		0.2451199165151e-09, 0.1166788435700e+01, 0.1435713242844e+03,
6261		0.2436734402904e-09, 0.3254726114901e+01, 0.2268582385539e+03,
6262		0.2213605274325e-09, 0.1687210598530e+01, 0.1658638954901e+03,
6263		0.1491521204829e-09, 0.2657541786794e+01, 0.2219950288015e+03,
6264		0.1474995329744e-09, 0.5013089805819e+01, 0.3052819430710e+03,
6265		0.1661939475656e-09, 0.5495315428418e+01, 0.2526661704812e+03,
6266
6267		0.9015946748003e-10, 0.2236989966505e+01, 0.4171445043968e+03 };
6268
6269		/* Sun-to-Earth, T^0, Z */
6270	2	static final double e0z[] = {
6271		0.2796207639075e-05, 0.3198701560209e+01, 0.8433466158131e+02,
6272		0.1016042198142e-05, 0.5422360395913e+01, 0.5507553240374e+01,
6273		0.8044305033647e-06, 0.3880222866652e+01, 0.5223693906222e+01,
6274		0.4385347909274e-06, 0.3704369937468e+01, 0.2352866153506e+01,
6275		0.3186156414906e-06, 0.3999639363235e+01, 0.1577343543434e+01,
6276		0.2272412285792e-06, 0.3984738315952e+01, 0.1047747311755e+01,
6277		0.1645620103007e-06, 0.3565412516841e+01, 0.5856477690889e+01,
6278		0.1815836921166e-06, 0.4984507059020e+01, 0.6283075850446e+01,
6279		0.1447461676364e-06, 0.3702753570108e+01, 0.9437762937313e+01,
6280		0.1430760876382e-06, 0.3409658712357e+01, 0.1021328554739e+02,
6281
6282		0.1120445753226e-06, 0.4829561570246e+01, 0.1414349524433e+02,
6283		0.1090232840797e-06, 0.2080729178066e+01, 0.6812766822558e+01,
6284		0.9715727346551e-07, 0.3476295881948e+01, 0.4694002934110e+01,
6285		0.1036267136217e-06, 0.4056639536648e+01, 0.7109288135493e+02,
6286		0.8752665271340e-07, 0.4448159519911e+01, 0.5753384878334e+01,
6287		0.8331864956004e-07, 0.4991704044208e+01, 0.7084896783808e+01,
6288		0.6901658670245e-07, 0.4325358994219e+01, 0.6275962395778e+01,
6289		0.9144536848998e-07, 0.1141826375363e+01, 0.6620890113188e+01,
6290		0.7205085037435e-07, 0.3624344170143e+01, 0.5296909721118e+00,
6291		0.7697874654176e-07, 0.5554257458998e+01, 0.1676215758509e+03,
6292
6293		0.5197545738384e-07, 0.6251760961735e+01, 0.1807370494127e+02,
6294		0.5031345378608e-07, 0.2497341091913e+01, 0.4705732307012e+01,
6295		0.4527110205840e-07, 0.2335079920992e+01, 0.6309374173736e+01,
6296		0.4753355798089e-07, 0.7094148987474e+00, 0.5884926831456e+01,
6297		0.4296951977516e-07, 0.1101916352091e+01, 0.6681224869435e+01,
6298		0.3855341568387e-07, 0.1825495405486e+01, 0.5486777812467e+01,
6299		0.5253930970990e-07, 0.4424740687208e+01, 0.7860419393880e+01,
6300		0.4024630496471e-07, 0.5120498157053e+01, 0.1336797263425e+02,
6301		0.4061069791453e-07, 0.6029771435451e+01, 0.3930209696940e+01,
6302		0.3797883804205e-07, 0.4435193600836e+00, 0.3154687086868e+01,
6303
6304		0.2933033225587e-07, 0.5124157356507e+01, 0.1059381944224e+01,
6305		0.3503000930426e-07, 0.5421830162065e+01, 0.6069776770667e+01,
6306		0.3670096214050e-07, 0.4582101667297e+01, 0.1219403291462e+02,
6307		0.2905609437008e-07, 0.1926566420072e+01, 0.1097707878456e+02,
6308		0.2466827821713e-07, 0.6090174539834e+00, 0.6496374930224e+01,
6309		0.2691647295332e-07, 0.1393432595077e+01, 0.2200391463820e+02,
6310		0.2150554667946e-07, 0.4308671715951e+01, 0.5643178611111e+01,
6311		0.2237481922680e-07, 0.8133968269414e+00, 0.8635942003952e+01,
6312		0.1817741038157e-07, 0.3755205127454e+01, 0.3340612434717e+01,
6313		0.2227820762132e-07, 0.2759558596664e+01, 0.1203646072878e+02,
6314
6315		0.1944713772307e-07, 0.5699645869121e+01, 0.1179062909082e+02,
6316		0.1527340520662e-07, 0.1986749091746e+01, 0.3981490189893e+00,
6317		0.1577282574914e-07, 0.3205017217983e+01, 0.5088628793478e+01,
6318		0.1424738825424e-07, 0.6256747903666e+01, 0.2544314396739e+01,
6319		0.1616563121701e-07, 0.2601671259394e+00, 0.1729818233119e+02,
6320		0.1401210391692e-07, 0.4686939173506e+01, 0.7058598460518e+01,
6321		0.1488726974214e-07, 0.2815862451372e+01, 0.2593412433514e+02,
6322		0.1692626442388e-07, 0.4956894109797e+01, 0.1564752902480e+03,
6323		0.1123571582910e-07, 0.2381192697696e+01, 0.3738761453707e+01,
6324		0.9903308606317e-08, 0.4294851657684e+01, 0.9225539266174e+01,
6325
6326		0.9174533187191e-08, 0.3075171510642e+01, 0.4164311961999e+01,
6327		0.8645985631457e-08, 0.5477534821633e+00, 0.8429241228195e+01,
6328		-0.1085876492688e-07, 0.0000000000000e+00, 0.0000000000000e+00,
6329		0.9264309077815e-08, 0.5968571670097e+01, 0.7079373888424e+01,
6330		0.8243116984954e-08, 0.1489098777643e+01, 0.1044738781244e+02,
6331		0.8268102113708e-08, 0.3512977691983e+01, 0.1150676975667e+02,
6332		0.9043613988227e-08, 0.1290704408221e+00, 0.1101510648075e+02,
6333		0.7432912038789e-08, 0.1991086893337e+01, 0.2608790314060e+02,
6334		0.8586233727285e-08, 0.4238357924414e+01, 0.2986433403208e+02,
6335		0.7612230060131e-08, 0.2911090150166e+01, 0.4732030630302e+01,
6336
6337		0.7097787751408e-08, 0.1908938392390e+01, 0.8031092209206e+01,
6338		0.7640237040175e-08, 0.6129219000168e+00, 0.7962980379786e+00,
6339		0.7070445688081e-08, 0.1380417036651e+01, 0.2146165377750e+01,
6340		0.7690770957702e-08, 0.1680504249084e+01, 0.2122839202813e+02,
6341		0.8051292542594e-08, 0.5127423484511e+01, 0.2942463415728e+01,
6342		0.5902709104515e-08, 0.2020274190917e+01, 0.7755226100720e+00,
6343		0.5134567496462e-08, 0.2606778676418e+01, 0.1256615170089e+02,
6344		0.5525802046102e-08, 0.1613011769663e+01, 0.8018209333619e+00,
6345		0.5880724784221e-08, 0.4604483417236e+01, 0.4690479774488e+01,
6346		0.5211699081370e-08, 0.5718964114193e+01, 0.8827390247185e+01,
6347
6348		0.4891849573562e-08, 0.3689658932196e+01, 0.2132990797783e+00,
6349		0.5150246069997e-08, 0.4099769855122e+01, 0.6480980550449e+02,
6350		0.5102434319633e-08, 0.5660834602509e+01, 0.3379454372902e+02,
6351		0.5083405254252e-08, 0.9842221218974e+00, 0.4136910472696e+01,
6352		0.4206562585682e-08, 0.1341363634163e+00, 0.3128388763578e+01,
6353		0.4663249683579e-08, 0.8130132735866e+00, 0.5216580451554e+01,
6354		0.4099474416530e-08, 0.5791497770644e+01, 0.4265981595566e+00,
6355		0.4628251220767e-08, 0.1249802769331e+01, 0.1572083878776e+02,
6356		0.5024068728142e-08, 0.4795684802743e+01, 0.6290189305114e+01,
6357		0.5120234327758e-08, 0.3810420387208e+01, 0.5230807360890e+01,
6358
6359		0.5524029815280e-08, 0.1029264714351e+01, 0.2397622045175e+03,
6360		0.4757415718860e-08, 0.3528044781779e+01, 0.1649636139783e+02,
6361		0.3915786131127e-08, 0.5593889282646e+01, 0.1589072916335e+01,
6362		0.4869053149991e-08, 0.3299636454433e+01, 0.7632943190217e+01,
6363		0.3649365703729e-08, 0.1286049002584e+01, 0.6206810014183e+01,
6364		0.3992493949002e-08, 0.3100307589464e+01, 0.2515860172507e+02,
6365		0.3320247477418e-08, 0.6212683940807e+01, 0.1216800268190e+02,
6366		0.3287123739696e-08, 0.4699118445928e+01, 0.7234794171227e+01,
6367		0.3472776811103e-08, 0.2630507142004e+01, 0.7342457794669e+01,
6368		0.3423253294767e-08, 0.2946432844305e+01, 0.9623688285163e+01,
6369
6370		0.3896173898244e-08, 0.1224834179264e+01, 0.6438496133249e+01,
6371		0.3388455337924e-08, 0.1543807616351e+01, 0.1494531617769e+02,
6372		0.3062704716523e-08, 0.1191777572310e+01, 0.8662240327241e+01,
6373		0.3270075600400e-08, 0.5483498767737e+01, 0.1194447056968e+01,
6374		0.3101209215259e-08, 0.8000833804348e+00, 0.3772475342596e+02,
6375		0.2780883347311e-08, 0.4077980721888e+00, 0.5863591145557e+01,
6376		0.2903605931824e-08, 0.2617490302147e+01, 0.1965104848470e+02,
6377		0.2682014743119e-08, 0.2634703158290e+01, 0.7238675589263e+01,
6378		0.2534360108492e-08, 0.6102446114873e+01, 0.6836645152238e+01,
6379		0.2392564882509e-08, 0.3681820208691e+01, 0.5849364236221e+01,
6380
6381		0.2656667254856e-08, 0.6216045388886e+01, 0.6133512519065e+01,
6382		0.2331242096773e-08, 0.5864949777744e+01, 0.4535059491685e+01,
6383		0.2287898363668e-08, 0.4566628532802e+01, 0.7477522907414e+01,
6384		0.2336944521306e-08, 0.2442722126930e+01, 0.1137170464392e+02,
6385		0.3156632236269e-08, 0.1626628050682e+01, 0.2509084901204e+03,
6386		0.2982612402766e-08, 0.2803604512609e+01, 0.1748016358760e+01,
6387		0.2774031674807e-08, 0.4654002897158e+01, 0.8223916695780e+02,
6388		0.2295236548638e-08, 0.4326518333253e+01, 0.3378142627421e+00,
6389		0.2190714699873e-08, 0.4519614578328e+01, 0.2908881142201e+02,
6390		0.2191495845045e-08, 0.3012626912549e+01, 0.1673046366289e+02,
6391
6392		0.2492901628386e-08, 0.1290101424052e+00, 0.1543797956245e+03,
6393		0.1993778064319e-08, 0.3864046799414e+01, 0.1778984560711e+02,
6394		0.1898146479022e-08, 0.5053777235891e+01, 0.2042657109477e+02,
6395		0.1918280127634e-08, 0.2222470192548e+01, 0.4165496312290e+02,
6396		0.1916351061607e-08, 0.8719067257774e+00, 0.7737595720538e+02,
6397		0.1834720181466e-08, 0.4031491098040e+01, 0.2358125818164e+02,
6398		0.1249201523806e-08, 0.5938379466835e+01, 0.3301902111895e+02,
6399		0.1477304050539e-08, 0.6544722606797e+00, 0.9548094718417e+02,
6400		0.1264316431249e-08, 0.2059072853236e+01, 0.8399684731857e+02,
6401		0.1203526495039e-08, 0.3644813532605e+01, 0.4558517281984e+02,
6402
6403		0.9221681059831e-09, 0.3241815055602e+01, 0.7805158573086e+02,
6404		0.7849278367646e-09, 0.5043812342457e+01, 0.5217580628120e+02,
6405		0.7983392077387e-09, 0.5000024502753e+01, 0.1501922143975e+03,
6406		0.7925395431654e-09, 0.1398734871821e-01, 0.9061773743175e+02,
6407		0.7640473285886e-09, 0.5067111723130e+01, 0.4951538251678e+02,
6408		0.5398937754482e-09, 0.5597382200075e+01, 0.1613385000004e+03,
6409		0.5626247550193e-09, 0.2601338209422e+01, 0.7318837597844e+02,
6410		0.5525197197855e-09, 0.5814832109256e+01, 0.1432335100216e+03,
6411		0.5407629837898e-09, 0.3384820609076e+01, 0.3230491187871e+03,
6412		0.3856739119801e-09, 0.1072391840473e+01, 0.2334791286671e+03,
6413
6414		0.3856425239987e-09, 0.2369540393327e+01, 0.1739046517013e+03,
6415		0.4350867755983e-09, 0.5255575751082e+01, 0.1620484330494e+03,
6416		0.3844113924996e-09, 0.5482356246182e+01, 0.9757644180768e+02,
6417		0.2854869155431e-09, 0.9573634763143e+00, 0.1697170704744e+03,
6418		0.1719227671416e-09, 0.1887203025202e+01, 0.2265204242912e+03,
6419		0.1527846879755e-09, 0.3982183931157e+01, 0.3341954043900e+03,
6420		0.1128229264847e-09, 0.2787457156298e+01, 0.3119028331842e+03 };
6421
6422		/* Sun-to-Earth, T^1, X */
6423	2	static final double e1x[] = {
6424		0.1234046326004e-05, 0.0000000000000e+00, 0.0000000000000e+00,
6425		0.5150068824701e-06, 0.6002664557501e+01, 0.1256615170089e+02,
6426		0.1290743923245e-07, 0.5959437664199e+01, 0.1884922755134e+02,
6427		0.1068615564952e-07, 0.2015529654209e+01, 0.6283075850446e+01,
6428		0.2079619142538e-08, 0.1732960531432e+01, 0.6279552690824e+01,
6429		0.2078009243969e-08, 0.4915604476996e+01, 0.6286599010068e+01,
6430		0.6206330058856e-09, 0.3616457953824e+00, 0.4705732307012e+01,
6431		0.5989335313746e-09, 0.3802607304474e+01, 0.6256777527156e+01,
6432		0.5958495663840e-09, 0.2845866560031e+01, 0.6309374173736e+01,
6433		0.4866923261539e-09, 0.5213203771824e+01, 0.7755226100720e+00,
6434
6435		0.4267785823142e-09, 0.4368189727818e+00, 0.1059381944224e+01,
6436		0.4610675141648e-09, 0.1837249181372e-01, 0.7860419393880e+01,
6437		0.3626989993973e-09, 0.2161590545326e+01, 0.5753384878334e+01,
6438		0.3563071194389e-09, 0.1452631954746e+01, 0.5884926831456e+01,
6439		0.3557015642807e-09, 0.4470593393054e+01, 0.6812766822558e+01,
6440		0.3210412089122e-09, 0.5195926078314e+01, 0.6681224869435e+01,
6441		0.2875473577986e-09, 0.5916256610193e+01, 0.2513230340178e+02,
6442		0.2842913681629e-09, 0.1149902426047e+01, 0.6127655567643e+01,
6443		0.2751248215916e-09, 0.5502088574662e+01, 0.6438496133249e+01,
6444		0.2481432881127e-09, 0.2921989846637e+01, 0.5486777812467e+01,
6445
6446		0.2059885976560e-09, 0.3718070376585e+01, 0.7079373888424e+01,
6447		0.2015522342591e-09, 0.5979395259740e+01, 0.6290189305114e+01,
6448		0.1995364084253e-09, 0.6772087985494e+00, 0.6275962395778e+01,
6449		0.1957436436943e-09, 0.2899210654665e+01, 0.5507553240374e+01,
6450		0.1651609818948e-09, 0.6228206482192e+01, 0.1150676975667e+02,
6451		0.1822980550699e-09, 0.1469348746179e+01, 0.1179062909082e+02,
6452		0.1675223159760e-09, 0.3813910555688e+01, 0.7058598460518e+01,
6453		0.1706491764745e-09, 0.3004380506684e+00, 0.7113454667900e-02,
6454		0.1392952362615e-09, 0.1440393973406e+01, 0.7962980379786e+00,
6455		0.1209868266342e-09, 0.4150425791727e+01, 0.4694002934110e+01,
6456
6457		0.1009827202611e-09, 0.3290040429843e+01, 0.3738761453707e+01,
6458		0.1047261388602e-09, 0.4229590090227e+01, 0.6282095334605e+01,
6459		0.1047006652004e-09, 0.2418967680575e+01, 0.6284056366286e+01,
6460		0.9609993143095e-10, 0.4627943659201e+01, 0.6069776770667e+01,
6461		0.9590900593873e-10, 0.1894393939924e+01, 0.4136910472696e+01,
6462		0.9146249188071e-10, 0.2010647519562e+01, 0.6496374930224e+01,
6463		0.8545274480290e-10, 0.5529846956226e-01, 0.1194447056968e+01,
6464		0.8224377881194e-10, 0.1254304102174e+01, 0.1589072916335e+01,
6465		0.6183529510410e-10, 0.3360862168815e+01, 0.8827390247185e+01,
6466		0.6259255147141e-10, 0.4755628243179e+01, 0.8429241228195e+01,
6467
6468		0.5539291694151e-10, 0.5371746955142e+01, 0.4933208510675e+01,
6469		0.7328259466314e-10, 0.4927699613906e+00, 0.4535059491685e+01,
6470		0.6017835843560e-10, 0.5776682001734e-01, 0.1255903824622e+02,
6471		0.7079827775243e-10, 0.4395059432251e+01, 0.5088628793478e+01,
6472		0.5170358878213e-10, 0.5154062619954e+01, 0.1176985366291e+02,
6473		0.4872301838682e-10, 0.6289611648973e+00, 0.6040347114260e+01,
6474		0.5249869411058e-10, 0.5617272046949e+01, 0.3154687086868e+01,
6475		0.4716172354411e-10, 0.3965901800877e+01, 0.5331357529664e+01,
6476		0.4871214940964e-10, 0.4627507050093e+01, 0.1256967486051e+02,
6477		0.4598076850751e-10, 0.6023631226459e+01, 0.6525804586632e+01,
6478
6479		0.4562196089485e-10, 0.4138562084068e+01, 0.3930209696940e+01,
6480		0.4325493872224e-10, 0.1330845906564e+01, 0.7632943190217e+01,
6481		0.5673781176748e-10, 0.2558752615657e+01, 0.5729506548653e+01,
6482		0.3961436642503e-10, 0.2728071734630e+01, 0.7234794171227e+01,
6483		0.5101868209058e-10, 0.4113444965144e+01, 0.6836645152238e+01,
6484		0.5257043167676e-10, 0.6195089830590e+01, 0.8031092209206e+01,
6485		0.5076613989393e-10, 0.2305124132918e+01, 0.7477522907414e+01,
6486		0.3342169352778e-10, 0.5415998155071e+01, 0.1097707878456e+02,
6487		0.3545881983591e-10, 0.3727160564574e+01, 0.4164311961999e+01,
6488		0.3364063738599e-10, 0.2901121049204e+00, 0.1137170464392e+02,
6489
6490		0.3357039670776e-10, 0.1652229354331e+01, 0.5223693906222e+01,
6491		0.4307412268687e-10, 0.4938909587445e+01, 0.1592596075957e+01,
6492		0.3405769115435e-10, 0.2408890766511e+01, 0.3128388763578e+01,
6493		0.3001926198480e-10, 0.4862239006386e+01, 0.1748016358760e+01,
6494		0.2778264787325e-10, 0.5241168661353e+01, 0.7342457794669e+01,
6495		0.2676159480666e-10, 0.3423593942199e+01, 0.2146165377750e+01,
6496		0.2954273399939e-10, 0.1881721265406e+01, 0.5368044267797e+00,
6497		0.3309362888795e-10, 0.1931525677349e+01, 0.8018209333619e+00,
6498		0.2810283608438e-10, 0.2414659495050e+01, 0.5225775174439e+00,
6499		0.3378045637764e-10, 0.4238019163430e+01, 0.1554202828031e+00,
6500
6501		0.2558134979840e-10, 0.1828225235805e+01, 0.5230807360890e+01,
6502		0.2273755578447e-10, 0.5858184283998e+01, 0.7084896783808e+01,
6503		0.2294176037690e-10, 0.4514589779057e+01, 0.1726015463500e+02,
6504		0.2533506099435e-10, 0.2355717851551e+01, 0.5216580451554e+01,
6505		0.2716685375812e-10, 0.2221003625100e+01, 0.8635942003952e+01,
6506		0.2419043435198e-10, 0.5955704951635e+01, 0.4690479774488e+01,
6507		0.2521232544812e-10, 0.1395676848521e+01, 0.5481254917084e+01,
6508		0.2630195021491e-10, 0.5727468918743e+01, 0.2629832328990e-01,
6509		0.2548395840944e-10, 0.2628351859400e-03, 0.1349867339771e+01 };
6510
6511		/* Sun-to-Earth, T^1, Y */
6512	2	static final double e1y[] = {
6513		0.9304690546528e-06, 0.0000000000000e+00, 0.0000000000000e+00,
6514		0.5150715570663e-06, 0.4431807116294e+01, 0.1256615170089e+02,
6515		0.1290825411056e-07, 0.4388610039678e+01, 0.1884922755134e+02,
6516		0.4645466665386e-08, 0.5827263376034e+01, 0.6283075850446e+01,
6517		0.2079625310718e-08, 0.1621698662282e+00, 0.6279552690824e+01,
6518		0.2078189850907e-08, 0.3344713435140e+01, 0.6286599010068e+01,
6519		0.6207190138027e-09, 0.5074049319576e+01, 0.4705732307012e+01,
6520		0.5989826532569e-09, 0.2231842216620e+01, 0.6256777527156e+01,
6521		0.5961360812618e-09, 0.1274975769045e+01, 0.6309374173736e+01,
6522		0.4874165471016e-09, 0.3642277426779e+01, 0.7755226100720e+00,
6523
6524		0.4283834034360e-09, 0.5148765510106e+01, 0.1059381944224e+01,
6525		0.4652389287529e-09, 0.4715794792175e+01, 0.7860419393880e+01,
6526		0.3751707476401e-09, 0.6617207370325e+00, 0.5753384878334e+01,
6527		0.3559998806198e-09, 0.6155548875404e+01, 0.5884926831456e+01,
6528		0.3558447558857e-09, 0.2898827297664e+01, 0.6812766822558e+01,
6529		0.3211116927106e-09, 0.3625813502509e+01, 0.6681224869435e+01,
6530		0.2875609914672e-09, 0.4345435813134e+01, 0.2513230340178e+02,
6531		0.2843109704069e-09, 0.5862263940038e+01, 0.6127655567643e+01,
6532		0.2744676468427e-09, 0.3926419475089e+01, 0.6438496133249e+01,
6533		0.2481285237789e-09, 0.1351976572828e+01, 0.5486777812467e+01,
6534
6535		0.2060338481033e-09, 0.2147556998591e+01, 0.7079373888424e+01,
6536		0.2015822358331e-09, 0.4408358972216e+01, 0.6290189305114e+01,
6537		0.2001195944195e-09, 0.5385829822531e+01, 0.6275962395778e+01,
6538		0.1953667642377e-09, 0.1304933746120e+01, 0.5507553240374e+01,
6539		0.1839744078713e-09, 0.6173567228835e+01, 0.1179062909082e+02,
6540		0.1643334294845e-09, 0.4635942997523e+01, 0.1150676975667e+02,
6541		0.1768051018652e-09, 0.5086283558874e+01, 0.7113454667900e-02,
6542		0.1674874205489e-09, 0.2243332137241e+01, 0.7058598460518e+01,
6543		0.1421445397609e-09, 0.6186899771515e+01, 0.7962980379786e+00,
6544		0.1255163958267e-09, 0.5730238465658e+01, 0.4694002934110e+01,
6545
6546		0.1013945281961e-09, 0.1726055228402e+01, 0.3738761453707e+01,
6547		0.1047294335852e-09, 0.2658801228129e+01, 0.6282095334605e+01,
6548		0.1047103879392e-09, 0.8481047835035e+00, 0.6284056366286e+01,
6549		0.9530343962826e-10, 0.3079267149859e+01, 0.6069776770667e+01,
6550		0.9604637611690e-10, 0.3258679792918e+00, 0.4136910472696e+01,
6551		0.9153518537177e-10, 0.4398599886584e+00, 0.6496374930224e+01,
6552		0.8562458214922e-10, 0.4772686794145e+01, 0.1194447056968e+01,
6553		0.8232525360654e-10, 0.5966220721679e+01, 0.1589072916335e+01,
6554		0.6150223411438e-10, 0.1780985591923e+01, 0.8827390247185e+01,
6555		0.6272087858000e-10, 0.3184305429012e+01, 0.8429241228195e+01,
6556
6557		0.5540476311040e-10, 0.3801260595433e+01, 0.4933208510675e+01,
6558		0.7331901699361e-10, 0.5205948591865e+01, 0.4535059491685e+01,
6559		0.6018528702791e-10, 0.4770139083623e+01, 0.1255903824622e+02,
6560		0.5150530724804e-10, 0.3574796899585e+01, 0.1176985366291e+02,
6561		0.6471933741811e-10, 0.2679787266521e+01, 0.5088628793478e+01,
6562		0.5317460644174e-10, 0.9528763345494e+00, 0.3154687086868e+01,
6563		0.4832187748783e-10, 0.5329322498232e+01, 0.6040347114260e+01,
6564		0.4716763555110e-10, 0.2395235316466e+01, 0.5331357529664e+01,
6565		0.4871509139861e-10, 0.3056663648823e+01, 0.1256967486051e+02,
6566		0.4598417696768e-10, 0.4452762609019e+01, 0.6525804586632e+01,
6567
6568		0.5674189533175e-10, 0.9879680872193e+00, 0.5729506548653e+01,
6569		0.4073560328195e-10, 0.5939127696986e+01, 0.7632943190217e+01,
6570		0.5040994945359e-10, 0.4549875824510e+01, 0.8031092209206e+01,
6571		0.5078185134679e-10, 0.7346659893982e+00, 0.7477522907414e+01,
6572		0.3769343537061e-10, 0.1071317188367e+01, 0.7234794171227e+01,
6573		0.4980331365299e-10, 0.2500345341784e+01, 0.6836645152238e+01,
6574		0.3458236594757e-10, 0.3825159450711e+01, 0.1097707878456e+02,
6575		0.3578859493602e-10, 0.5299664791549e+01, 0.4164311961999e+01,
6576		0.3370504646419e-10, 0.5002316301593e+01, 0.1137170464392e+02,
6577		0.3299873338428e-10, 0.2526123275282e+01, 0.3930209696940e+01,
6578
6579		0.4304917318409e-10, 0.3368078557132e+01, 0.1592596075957e+01,
6580		0.3402418753455e-10, 0.8385495425800e+00, 0.3128388763578e+01,
6581		0.2778460572146e-10, 0.3669905203240e+01, 0.7342457794669e+01,
6582		0.2782710128902e-10, 0.2691664812170e+00, 0.1748016358760e+01,
6583		0.2711725179646e-10, 0.4707487217718e+01, 0.5296909721118e+00,
6584		0.2981760946340e-10, 0.3190260867816e+00, 0.5368044267797e+00,
6585		0.2811672977772e-10, 0.3196532315372e+01, 0.7084896783808e+01,
6586		0.2863454474467e-10, 0.2263240324780e+00, 0.5223693906222e+01,
6587		0.3333464634051e-10, 0.3498451685065e+01, 0.8018209333619e+00,
6588		0.3312991747609e-10, 0.5839154477412e+01, 0.1554202828031e+00,
6589
6590		0.2813255564006e-10, 0.8268044346621e+00, 0.5225775174439e+00,
6591		0.2665098083966e-10, 0.3934021725360e+01, 0.5216580451554e+01,
6592		0.2349795705216e-10, 0.5197620913779e+01, 0.2146165377750e+01,
6593		0.2330352293961e-10, 0.2984999231807e+01, 0.1726015463500e+02,
6594		0.2728001683419e-10, 0.6521679638544e+00, 0.8635942003952e+01,
6595		0.2484061007669e-10, 0.3468955561097e+01, 0.5230807360890e+01,
6596		0.2646328768427e-10, 0.1013724533516e+01, 0.2629832328990e-01,
6597		0.2518630264831e-10, 0.6108081057122e+01, 0.5481254917084e+01,
6598		0.2421901455384e-10, 0.1651097776260e+01, 0.1349867339771e+01,
6599		0.6348533267831e-11, 0.3220226560321e+01, 0.8433466158131e+02 };
6600
6601		/* Sun-to-Earth, T^1, Z */
6602	2	static final double e1z[] = {
6603		0.2278290449966e-05, 0.3413716033863e+01, 0.6283075850446e+01,
6604		0.5429458209830e-07, 0.0000000000000e+00, 0.0000000000000e+00,
6605		0.1903240492525e-07, 0.3370592358297e+01, 0.1256615170089e+02,
6606		0.2385409276743e-09, 0.3327914718416e+01, 0.1884922755134e+02,
6607		0.8676928342573e-10, 0.1824006811264e+01, 0.5223693906222e+01,
6608		0.7765442593544e-10, 0.3888564279247e+01, 0.5507553240374e+01,
6609		0.7066158332715e-10, 0.5194267231944e+01, 0.2352866153506e+01,
6610		0.7092175288657e-10, 0.2333246960021e+01, 0.8399684731857e+02,
6611		0.5357582213535e-10, 0.2224031176619e+01, 0.5296909721118e+00,
6612		0.3828035865021e-10, 0.2156710933584e+01, 0.6279552690824e+01,
6613
6614		0.3824857220427e-10, 0.1529755219915e+01, 0.6286599010068e+01,
6615		0.3286995181628e-10, 0.4879512900483e+01, 0.1021328554739e+02 };
6616
6617		/* Sun-to-Earth, T^2, X */
6618	2	static final double e2x[] = {
6619		-0.4143818297913e-10, 0.0000000000000e+00, 0.0000000000000e+00,
6620		0.2171497694435e-10, 0.4398225628264e+01, 0.1256615170089e+02,
6621		0.9845398442516e-11, 0.2079720838384e+00, 0.6283075850446e+01,
6622		0.9256833552682e-12, 0.4191264694361e+01, 0.1884922755134e+02,
6623		0.1022049384115e-12, 0.5381133195658e+01, 0.8399684731857e+02 };
6624
6625		/* Sun-to-Earth, T^2, Y */
6626	2	static final double e2y[] = {
6627		0.5063375872532e-10, 0.0000000000000e+00, 0.0000000000000e+00,
6628		0.2173815785980e-10, 0.2827805833053e+01, 0.1256615170089e+02,
6629		0.1010231999920e-10, 0.4634612377133e+01, 0.6283075850446e+01,
6630		0.9259745317636e-12, 0.2620612076189e+01, 0.1884922755134e+02,
6631		0.1022202095812e-12, 0.3809562326066e+01, 0.8399684731857e+02 };
6632
6633		/* Sun-to-Earth, T^2, Z */
6634	2	static final double e2z[] = {
6635		0.9722666114891e-10, 0.5152219582658e+01, 0.6283075850446e+01,
6636		-0.3494819171909e-11, 0.0000000000000e+00, 0.0000000000000e+00,
6637		0.6713034376076e-12, 0.6440188750495e+00, 0.1256615170089e+02 };
6638
6639		}
6640		//subclassed the
6641	0	private static class SSB {
6642		/* SSB-to-Sun, T^0, X */
6643	2	static final double s0x[] = {
6644		0.4956757536410e-02, 0.3741073751789e+01, 0.5296909721118e+00,
6645		0.2718490072522e-02, 0.4016011511425e+01, 0.2132990797783e+00,
6646		0.1546493974344e-02, 0.2170528330642e+01, 0.3813291813120e-01,
6647		0.8366855276341e-03, 0.2339614075294e+01, 0.7478166569050e-01,
6648		0.2936777942117e-03, 0.0000000000000e+00, 0.0000000000000e+00,
6649		0.1201317439469e-03, 0.4090736353305e+01, 0.1059381944224e+01,
6650		0.7578550887230e-04, 0.3241518088140e+01, 0.4265981595566e+00,
6651		0.1941787367773e-04, 0.1012202064330e+01, 0.2061856251104e+00,
6652		0.1889227765991e-04, 0.3892520416440e+01, 0.2204125344462e+00,
6653		0.1937896968613e-04, 0.4797779441161e+01, 0.1495633313810e+00,
6654
6655		0.1434506110873e-04, 0.3868960697933e+01, 0.5225775174439e+00,
6656		0.1406659911580e-04, 0.4759766557397e+00, 0.5368044267797e+00,
6657		0.1179022300202e-04, 0.7774961520598e+00, 0.7626583626240e-01,
6658		0.8085864460959e-05, 0.3254654471465e+01, 0.3664874755930e-01,
6659		0.7622752967615e-05, 0.4227633103489e+01, 0.3961708870310e-01,
6660		0.6209171139066e-05, 0.2791828325711e+00, 0.7329749511860e-01,
6661		0.4366435633970e-05, 0.4440454875925e+01, 0.1589072916335e+01,
6662		0.3792124889348e-05, 0.5156393842356e+01, 0.7113454667900e-02,
6663		0.3154548963402e-05, 0.6157005730093e+01, 0.4194847048887e+00,
6664		0.3088359882942e-05, 0.2494567553163e+01, 0.6398972393349e+00,
6665
6666		0.2788440902136e-05, 0.4934318747989e+01, 0.1102062672231e+00,
6667		0.3039928456376e-05, 0.4895077702640e+01, 0.6283075850446e+01,
6668		0.2272258457679e-05, 0.5278394064764e+01, 0.1030928125552e+00,
6669		0.2162007057957e-05, 0.5802978019099e+01, 0.3163918923335e+00,
6670		0.1767632855737e-05, 0.3415346595193e-01, 0.1021328554739e+02,
6671		0.1349413459362e-05, 0.2001643230755e+01, 0.1484170571900e-02,
6672		0.1170141900476e-05, 0.2424750491620e+01, 0.6327837846670e+00,
6673		0.1054355266820e-05, 0.3123311487576e+01, 0.4337116142245e+00,
6674		0.9800822461610e-06, 0.3026258088130e+01, 0.1052268489556e+01,
6675		0.1091203749931e-05, 0.3157811670347e+01, 0.1162474756779e+01,
6676
6677		0.6960236715913e-06, 0.8219570542313e+00, 0.1066495398892e+01,
6678		0.5689257296909e-06, 0.1323052375236e+01, 0.9491756770005e+00,
6679		0.6613172135802e-06, 0.2765348881598e+00, 0.8460828644453e+00,
6680		0.6277702517571e-06, 0.5794064466382e+01, 0.1480791608091e+00,
6681		0.6304884066699e-06, 0.7323555380787e+00, 0.2243449970715e+00,
6682		0.4897850467382e-06, 0.3062464235399e+01, 0.3340612434717e+01,
6683		0.3759148598786e-06, 0.4588290469664e+01, 0.3516457698740e-01,
6684		0.3110520548195e-06, 0.1374299536572e+01, 0.6373574839730e-01,
6685		0.3064708359780e-06, 0.4222267485047e+01, 0.1104591729320e-01,
6686		0.2856347168241e-06, 0.3714202944973e+01, 0.1510475019529e+00,
6687
6688		0.2840945514288e-06, 0.2847972875882e+01, 0.4110125927500e-01,
6689		0.2378951599405e-06, 0.3762072563388e+01, 0.2275259891141e+00,
6690		0.2714229481417e-06, 0.1036049980031e+01, 0.2535050500000e-01,
6691		0.2323551717307e-06, 0.4682388599076e+00, 0.8582758298370e-01,
6692		0.1881790512219e-06, 0.4790565425418e+01, 0.2118763888447e+01,
6693		0.2261353968371e-06, 0.1669144912212e+01, 0.7181332454670e-01,
6694		0.2214546389848e-06, 0.3937717281614e+01, 0.2968341143800e-02,
6695		0.2184915594933e-06, 0.1129169845099e+00, 0.7775000683430e-01,
6696		0.2000164937936e-06, 0.4030009638488e+01, 0.2093666171530e+00,
6697		0.1966105136719e-06, 0.8745955786834e+00, 0.2172315424036e+00,
6698
6699		0.1904742332624e-06, 0.5919743598964e+01, 0.2022531624851e+00,
6700		0.1657399705031e-06, 0.2549141484884e+01, 0.7358765972222e+00,
6701		0.1574070533987e-06, 0.5277533020230e+01, 0.7429900518901e+00,
6702		0.1832261651039e-06, 0.3064688127777e+01, 0.3235053470014e+00,
6703		0.1733615346569e-06, 0.3011432799094e+01, 0.1385174140878e+00,
6704		0.1549124014496e-06, 0.4005569132359e+01, 0.5154640627760e+00,
6705		0.1637044713838e-06, 0.1831375966632e+01, 0.8531963191132e+00,
6706		0.1123420082383e-06, 0.1180270407578e+01, 0.1990721704425e+00,
6707		0.1083754165740e-06, 0.3414101320863e+00, 0.5439178814476e+00,
6708		0.1156638012655e-06, 0.6130479452594e+00, 0.5257585094865e+00,
6709
6710		0.1142548785134e-06, 0.3724761948846e+01, 0.5336234347371e+00,
6711		0.7921463895965e-07, 0.2435425589361e+01, 0.1478866649112e+01,
6712		0.7428600285231e-07, 0.3542144398753e+01, 0.2164800718209e+00,
6713		0.8323211246747e-07, 0.3525058072354e+01, 0.1692165728891e+01,
6714		0.7257595116312e-07, 0.1364299431982e+01, 0.2101180877357e+00,
6715		0.7111185833236e-07, 0.2460478875808e+01, 0.4155522422634e+00,
6716		0.6868090383716e-07, 0.4397327670704e+01, 0.1173197218910e+00,
6717		0.7226419974175e-07, 0.4042647308905e+01, 0.1265567569334e+01,
6718		0.6955642383177e-07, 0.2865047906085e+01, 0.9562891316684e+00,
6719		0.7492139296331e-07, 0.5014278994215e+01, 0.1422690933580e-01,
6720
6721		0.6598363128857e-07, 0.2376730020492e+01, 0.6470106940028e+00,
6722		0.7381147293385e-07, 0.3272990384244e+01, 0.1581959461667e+01,
6723		0.6402909624032e-07, 0.5302290955138e+01, 0.9597935788730e-01,
6724		0.6237454263857e-07, 0.5444144425332e+01, 0.7084920306520e-01,
6725		0.5241198544016e-07, 0.4215359579205e+01, 0.5265099800692e+00,
6726		0.5144463853918e-07, 0.1218916689916e+00, 0.5328719641544e+00,
6727		0.5868164772299e-07, 0.2369402002213e+01, 0.7871412831580e-01,
6728		0.6233195669151e-07, 0.1254922242403e+01, 0.2608790314060e+02,
6729		0.6068463791422e-07, 0.5679713760431e+01, 0.1114304132498e+00,
6730		0.4359361135065e-07, 0.6097219641646e+00, 0.1375773836557e+01,
6731
6732		0.4686510366826e-07, 0.4786231041431e+01, 0.1143987543936e+00,
6733		0.3758977287225e-07, 0.1167368068139e+01, 0.1596186371003e+01,
6734		0.4282051974778e-07, 0.1519471064319e+01, 0.2770348281756e+00,
6735		0.5153765386113e-07, 0.1860532322984e+01, 0.2228608264996e+00,
6736		0.4575129387188e-07, 0.7632857887158e+00, 0.1465949902372e+00,
6737		0.3326844933286e-07, 0.1298219485285e+01, 0.5070101000000e-01,
6738		0.3748617450984e-07, 0.1046510321062e+01, 0.4903339079539e+00,
6739		0.2816756661499e-07, 0.3434522346190e+01, 0.2991266627620e+00,
6740		0.3412750405039e-07, 0.2523766270318e+01, 0.3518164938661e+00,
6741		0.2655796761776e-07, 0.2904422260194e+01, 0.6256703299991e+00,
6742
6743		0.2963597929458e-07, 0.5923900431149e+00, 0.1099462426779e+00,
6744		0.2539523734781e-07, 0.4851947722567e+01, 0.1256615170089e+02,
6745		0.2283087914139e-07, 0.3400498595496e+01, 0.6681224869435e+01,
6746		0.2321309799331e-07, 0.5789099148673e+01, 0.3368040641550e-01,
6747		0.2549657649750e-07, 0.3991856479792e-01, 0.1169588211447e+01,
6748		0.2290462303977e-07, 0.2788567577052e+01, 0.1045155034888e+01,
6749		0.1945398522914e-07, 0.3290896998176e+01, 0.1155361302111e+01,
6750		0.1849171512638e-07, 0.2698060129367e+01, 0.4452511715700e-02,
6751		0.1647199834254e-07, 0.3016735644085e+01, 0.4408250688924e+00,
6752		0.1529530765273e-07, 0.5573043116178e+01, 0.6521991896920e-01,
6753
6754		0.1433199339978e-07, 0.1481192356147e+01, 0.9420622223326e+00,
6755		0.1729134193602e-07, 0.1422817538933e+01, 0.2108507877249e+00,
6756		0.1716463931346e-07, 0.3469468901855e+01, 0.2157473718317e+00,
6757		0.1391206061378e-07, 0.6122436220547e+01, 0.4123712502208e+00,
6758		0.1404746661924e-07, 0.1647765641936e+01, 0.4258542984690e-01,
6759		0.1410452399455e-07, 0.5989729161964e+01, 0.2258291676434e+00,
6760		0.1089828772168e-07, 0.2833705509371e+01, 0.4226656969313e+00,
6761		0.1047374564948e-07, 0.5090690007331e+00, 0.3092784376656e+00,
6762		0.1358279126532e-07, 0.5128990262836e+01, 0.7923417740620e-01,
6763		0.1020456476148e-07, 0.9632772880808e+00, 0.1456308687557e+00,
6764
6765		0.1033428735328e-07, 0.3223779318418e+01, 0.1795258541446e+01,
6766		0.1412435841540e-07, 0.2410271572721e+01, 0.1525316725248e+00,
6767		0.9722759371574e-08, 0.2333531395690e+01, 0.8434341241180e-01,
6768		0.9657334084704e-08, 0.6199270974168e+01, 0.1272681024002e+01,
6769		0.1083641148690e-07, 0.2864222292929e+01, 0.7032915397480e-01,
6770		0.1067318403838e-07, 0.5833458866568e+00, 0.2123349582968e+00,
6771		0.1062366201976e-07, 0.4307753989494e+01, 0.2142632012598e+00,
6772		0.1236364149266e-07, 0.2873917870593e+01, 0.1847279083684e+00,
6773		0.1092759489593e-07, 0.2959887266733e+01, 0.1370332435159e+00,
6774		0.8912069362899e-08, 0.5141213702562e+01, 0.2648454860559e+01,
6775
6776		0.9656467707970e-08, 0.4532182462323e+01, 0.4376440768498e+00,
6777		0.8098386150135e-08, 0.2268906338379e+01, 0.2880807454688e+00,
6778		0.7857714675000e-08, 0.4055544260745e+01, 0.2037373330570e+00,
6779		0.7288455940646e-08, 0.5357901655142e+01, 0.1129145838217e+00,
6780		0.9450595950552e-08, 0.4264926963939e+01, 0.5272426800584e+00,
6781		0.9381718247537e-08, 0.7489366976576e-01, 0.5321392641652e+00,
6782		0.7079052646038e-08, 0.1923311052874e+01, 0.6288513220417e+00,
6783		0.9259004415344e-08, 0.2970256853438e+01, 0.1606092486742e+00,
6784		0.8259801499742e-08, 0.3327056314697e+01, 0.8389694097774e+00,
6785		0.6476334355779e-08, 0.2954925505727e+01, 0.2008557621224e+01,
6786
6787		0.5984021492007e-08, 0.9138753105829e+00, 0.2042657109477e+02,
6788		0.5989546863181e-08, 0.3244464082031e+01, 0.2111650433779e+01,
6789		0.6233108606023e-08, 0.4995232638403e+00, 0.4305306221819e+00,
6790		0.6877299149965e-08, 0.2834987233449e+01, 0.9561746721300e-02,
6791		0.8311234227190e-08, 0.2202951835758e+01, 0.3801276407308e+00,
6792		0.6599472832414e-08, 0.4478581462618e+01, 0.1063314406849e+01,
6793		0.6160491096549e-08, 0.5145858696411e+01, 0.1368660381889e+01,
6794		0.6164772043891e-08, 0.3762976697911e+00, 0.4234171675140e+00,
6795		0.6363248684450e-08, 0.3162246718685e+01, 0.1253008786510e-01,
6796		0.6448587520999e-08, 0.3442693302119e+01, 0.5287268506303e+00,
6797
6798		0.6431662283977e-08, 0.8977549136606e+00, 0.5306550935933e+00,
6799		0.6351223158474e-08, 0.4306447410369e+01, 0.5217580628120e+02,
6800		0.5476721393451e-08, 0.3888529177855e+01, 0.2221856701002e+01,
6801		0.5341772572619e-08, 0.2655560662512e+01, 0.7466759693650e-01,
6802		0.5337055758302e-08, 0.5164990735946e+01, 0.7489573444450e-01,
6803		0.5373120816787e-08, 0.6041214553456e+01, 0.1274714967946e+00,
6804		0.5392351705426e-08, 0.9177763485932e+00, 0.1055449481598e+01,
6805		0.6688495850205e-08, 0.3089608126937e+01, 0.2213766559277e+00,
6806		0.5072003660362e-08, 0.4311316541553e+01, 0.2132517061319e+00,
6807		0.5070726650455e-08, 0.5790675464444e+00, 0.2133464534247e+00,
6808
6809		0.5658012950032e-08, 0.2703945510675e+01, 0.7287631425543e+00,
6810		0.4835509924854e-08, 0.2975422976065e+01, 0.7160067364790e-01,
6811		0.6479821978012e-08, 0.1324168733114e+01, 0.2209183458640e-01,
6812		0.6230636494980e-08, 0.2860103632836e+01, 0.3306188016693e+00,
6813		0.4649239516213e-08, 0.4832259763403e+01, 0.7796265773310e-01,
6814		0.6487325792700e-08, 0.2726165825042e+01, 0.3884652414254e+00,
6815		0.4682823682770e-08, 0.6966602455408e+00, 0.1073608853559e+01,
6816		0.5704230804976e-08, 0.5669634104606e+01, 0.8731175355560e-01,
6817		0.6125413585489e-08, 0.1513386538915e+01, 0.7605151500000e-01,
6818		0.6035825038187e-08, 0.1983509168227e+01, 0.9846002785331e+00,
6819
6820		0.4331123462303e-08, 0.2782892992807e+01, 0.4297791515992e+00,
6821		0.4681107685143e-08, 0.5337232886836e+01, 0.2127790306879e+00,
6822		0.4669105829655e-08, 0.5837133792160e+01, 0.2138191288687e+00,
6823		0.5138823602365e-08, 0.3080560200507e+01, 0.7233337363710e-01,
6824		0.4615856664534e-08, 0.1661747897471e+01, 0.8603097737811e+00,
6825		0.4496916702197e-08, 0.2112508027068e+01, 0.7381754420900e-01,
6826		0.4278479042945e-08, 0.5716528462627e+01, 0.7574578717200e-01,
6827		0.3840525503932e-08, 0.6424172726492e+00, 0.3407705765729e+00,
6828		0.4866636509685e-08, 0.4919244697715e+01, 0.7722995774390e-01,
6829		0.3526100639296e-08, 0.2550821052734e+01, 0.6225157782540e-01,
6830
6831		0.3939558488075e-08, 0.3939331491710e+01, 0.5268983110410e-01,
6832		0.4041268772576e-08, 0.2275337571218e+01, 0.3503323232942e+00,
6833		0.3948761842853e-08, 0.1999324200790e+01, 0.1451108196653e+00,
6834		0.3258394550029e-08, 0.9121001378200e+00, 0.5296435984654e+00,
6835		0.3257897048761e-08, 0.3428428660869e+01, 0.5297383457582e+00,
6836		0.3842559031298e-08, 0.6132927720035e+01, 0.9098186128426e+00,
6837		0.3109920095448e-08, 0.7693650193003e+00, 0.3932462625300e-02,
6838		0.3132237775119e-08, 0.3621293854908e+01, 0.2346394437820e+00,
6839		0.3942189421510e-08, 0.4841863659733e+01, 0.3180992042600e-02,
6840		0.3796972285340e-08, 0.1814174994268e+01, 0.1862120789403e+00,
6841
6842		0.3995640233688e-08, 0.1386990406091e+01, 0.4549093064213e+00,
6843		0.2875013727414e-08, 0.9178318587177e+00, 0.1905464808669e+01,
6844		0.3073719932844e-08, 0.2688923811835e+01, 0.3628624111593e+00,
6845		0.2731016580075e-08, 0.1188259127584e+01, 0.2131850110243e+00,
6846		0.2729549896546e-08, 0.3702160634273e+01, 0.2134131485323e+00,
6847		0.3339372892449e-08, 0.7199163960331e+00, 0.2007689919132e+00,
6848		0.2898833764204e-08, 0.1916709364999e+01, 0.5291709230214e+00,
6849		0.2894536549362e-08, 0.2424043195547e+01, 0.5302110212022e+00,
6850		0.3096872473843e-08, 0.4445894977497e+01, 0.2976424921901e+00,
6851		0.2635672326810e-08, 0.3814366984117e+01, 0.1485980103780e+01,
6852
6853		0.3649302697001e-08, 0.2924200596084e+01, 0.6044726378023e+00,
6854		0.3127954585895e-08, 0.1842251648327e+01, 0.1084620721060e+00,
6855		0.2616040173947e-08, 0.4155841921984e+01, 0.1258454114666e+01,
6856		0.2597395859860e-08, 0.1158045978874e+00, 0.2103781122809e+00,
6857		0.2593286172210e-08, 0.4771850408691e+01, 0.2162200472757e+00,
6858		0.2481823585747e-08, 0.4608842558889e+00, 0.1062562936266e+01,
6859		0.2742219550725e-08, 0.1538781127028e+01, 0.5651155736444e+00,
6860		0.3199558469610e-08, 0.3226647822878e+00, 0.7036329877322e+00,
6861		0.2666088542957e-08, 0.1967991731219e+00, 0.1400015846597e+00,
6862		0.2397067430580e-08, 0.3707036669873e+01, 0.2125476091956e+00,
6863
6864		0.2376570772738e-08, 0.1182086628042e+01, 0.2140505503610e+00,
6865		0.2547228007887e-08, 0.4906256820629e+01, 0.1534957940063e+00,
6866		0.2265575594114e-08, 0.3414949866857e+01, 0.2235935264888e+00,
6867		0.2464381430585e-08, 0.4599122275378e+01, 0.2091065926078e+00,
6868		0.2433408527044e-08, 0.2830751145445e+00, 0.2174915669488e+00,
6869		0.2443605509076e-08, 0.4212046432538e+01, 0.1739420156204e+00,
6870		0.2319779262465e-08, 0.9881978408630e+00, 0.7530171478090e-01,
6871		0.2284622835465e-08, 0.5565347331588e+00, 0.7426161660010e-01,
6872		0.2467268750783e-08, 0.5655708150766e+00, 0.2526561439362e+00,
6873		0.2808513492782e-08, 0.1418405053408e+01, 0.5636314030725e+00,
6874
6875		0.2329528932532e-08, 0.4069557545675e+01, 0.1056200952181e+01,
6876		0.9698639532817e-09, 0.1074134313634e+01, 0.7826370942180e+02 };
6877
6878		/* SSB-to-Sun, T^0, Y */
6879	2	static final double s0y[] = {
6880		0.4955392320126e-02, 0.2170467313679e+01, 0.5296909721118e+00,
6881		0.2722325167392e-02, 0.2444433682196e+01, 0.2132990797783e+00,
6882		0.1546579925346e-02, 0.5992779281546e+00, 0.3813291813120e-01,
6883		0.8363140252966e-03, 0.7687356310801e+00, 0.7478166569050e-01,
6884		0.3385792683603e-03, 0.0000000000000e+00, 0.0000000000000e+00,
6885		0.1201192221613e-03, 0.2520035601514e+01, 0.1059381944224e+01,
6886		0.7587125720554e-04, 0.1669954006449e+01, 0.4265981595566e+00,
6887		0.1964155361250e-04, 0.5707743963343e+01, 0.2061856251104e+00,
6888		0.1891900364909e-04, 0.2320960679937e+01, 0.2204125344462e+00,
6889		0.1937373433356e-04, 0.3226940689555e+01, 0.1495633313810e+00,
6890
6891		0.1437139941351e-04, 0.2301626908096e+01, 0.5225775174439e+00,
6892		0.1406267683099e-04, 0.5188579265542e+01, 0.5368044267797e+00,
6893		0.1178703080346e-04, 0.5489483248476e+01, 0.7626583626240e-01,
6894		0.8079835186041e-05, 0.1683751835264e+01, 0.3664874755930e-01,
6895		0.7623253594652e-05, 0.2656400462961e+01, 0.3961708870310e-01,
6896		0.6248667483971e-05, 0.4992775362055e+01, 0.7329749511860e-01,
6897		0.4366353695038e-05, 0.2869706279678e+01, 0.1589072916335e+01,
6898		0.3829101568895e-05, 0.3572131359950e+01, 0.7113454667900e-02,
6899		0.3175733773908e-05, 0.4535372530045e+01, 0.4194847048887e+00,
6900		0.3092437902159e-05, 0.9230153317909e+00, 0.6398972393349e+00,
6901
6902		0.2874168812154e-05, 0.3363143761101e+01, 0.1102062672231e+00,
6903		0.3040119321826e-05, 0.3324250895675e+01, 0.6283075850446e+01,
6904		0.2699723308006e-05, 0.2917882441928e+00, 0.1030928125552e+00,
6905		0.2134832683534e-05, 0.4220997202487e+01, 0.3163918923335e+00,
6906		0.1770412139433e-05, 0.4747318496462e+01, 0.1021328554739e+02,
6907		0.1377264209373e-05, 0.4305058462401e+00, 0.1484170571900e-02,
6908		0.1127814538960e-05, 0.8538177240740e+00, 0.6327837846670e+00,
6909		0.1055608090130e-05, 0.1551800742580e+01, 0.4337116142245e+00,
6910		0.9802673861420e-06, 0.1459646735377e+01, 0.1052268489556e+01,
6911		0.1090329461951e-05, 0.1587351228711e+01, 0.1162474756779e+01,
6912
6913		0.6959590025090e-06, 0.5534442628766e+01, 0.1066495398892e+01,
6914		0.5664914529542e-06, 0.6030673003297e+01, 0.9491756770005e+00,
6915		0.6607787763599e-06, 0.4989507233927e+01, 0.8460828644453e+00,
6916		0.6269725742838e-06, 0.4222951804572e+01, 0.1480791608091e+00,
6917		0.6301889697863e-06, 0.5444316669126e+01, 0.2243449970715e+00,
6918		0.4891042662861e-06, 0.1490552839784e+01, 0.3340612434717e+01,
6919		0.3457083123290e-06, 0.3030475486049e+01, 0.3516457698740e-01,
6920		0.3032559967314e-06, 0.2652038793632e+01, 0.1104591729320e-01,
6921		0.2841133988903e-06, 0.1276744786829e+01, 0.4110125927500e-01,
6922		0.2855564444432e-06, 0.2143368674733e+01, 0.1510475019529e+00,
6923
6924		0.2765157135038e-06, 0.5444186109077e+01, 0.6373574839730e-01,
6925		0.2382312465034e-06, 0.2190521137593e+01, 0.2275259891141e+00,
6926		0.2808060365077e-06, 0.5735195064841e+01, 0.2535050500000e-01,
6927		0.2332175234405e-06, 0.9481985524859e-01, 0.7181332454670e-01,
6928		0.2322488199659e-06, 0.5180499361533e+01, 0.8582758298370e-01,
6929		0.1881850258423e-06, 0.3219788273885e+01, 0.2118763888447e+01,
6930		0.2196111392808e-06, 0.2366941159761e+01, 0.2968341143800e-02,
6931		0.2183810335519e-06, 0.4825445110915e+01, 0.7775000683430e-01,
6932		0.2002733093326e-06, 0.2457148995307e+01, 0.2093666171530e+00,
6933		0.1967111767229e-06, 0.5586291545459e+01, 0.2172315424036e+00,
6934
6935		0.1568473250543e-06, 0.3708003123320e+01, 0.7429900518901e+00,
6936		0.1852528314300e-06, 0.4310638151560e+01, 0.2022531624851e+00,
6937		0.1832111226447e-06, 0.1494665322656e+01, 0.3235053470014e+00,
6938		0.1746805502310e-06, 0.1451378500784e+01, 0.1385174140878e+00,
6939		0.1555730966650e-06, 0.1068040418198e+01, 0.7358765972222e+00,
6940		0.1554883462559e-06, 0.2442579035461e+01, 0.5154640627760e+00,
6941		0.1638380568746e-06, 0.2597913420625e+00, 0.8531963191132e+00,
6942		0.1159938593640e-06, 0.5834512021280e+01, 0.1990721704425e+00,
6943		0.1083427965695e-06, 0.5054033177950e+01, 0.5439178814476e+00,
6944		0.1156480369431e-06, 0.5325677432457e+01, 0.5257585094865e+00,
6945
6946		0.1141308860095e-06, 0.2153403923857e+01, 0.5336234347371e+00,
6947		0.7913146470946e-07, 0.8642846847027e+00, 0.1478866649112e+01,
6948		0.7439752463733e-07, 0.1970628496213e+01, 0.2164800718209e+00,
6949		0.7280277104079e-07, 0.6073307250609e+01, 0.2101180877357e+00,
6950		0.8319567719136e-07, 0.1954371928334e+01, 0.1692165728891e+01,
6951		0.7137705549290e-07, 0.8904989440909e+00, 0.4155522422634e+00,
6952		0.6900825396225e-07, 0.2825717714977e+01, 0.1173197218910e+00,
6953		0.7245757216635e-07, 0.2481677513331e+01, 0.1265567569334e+01,
6954		0.6961165696255e-07, 0.1292955312978e+01, 0.9562891316684e+00,
6955		0.7571804456890e-07, 0.3427517575069e+01, 0.1422690933580e-01,
6956
6957		0.6605425721904e-07, 0.8052192701492e+00, 0.6470106940028e+00,
6958		0.7375477357248e-07, 0.1705076390088e+01, 0.1581959461667e+01,
6959		0.7041664951470e-07, 0.4848356967891e+00, 0.9597935788730e-01,
6960		0.6322199535763e-07, 0.3878069473909e+01, 0.7084920306520e-01,
6961		0.5244380279191e-07, 0.2645560544125e+01, 0.5265099800692e+00,
6962		0.5143125704988e-07, 0.4834486101370e+01, 0.5328719641544e+00,
6963		0.5871866319373e-07, 0.7981472548900e+00, 0.7871412831580e-01,
6964		0.6300822573871e-07, 0.5979398788281e+01, 0.2608790314060e+02,
6965		0.6062154271548e-07, 0.4108655402756e+01, 0.1114304132498e+00,
6966		0.4361912339976e-07, 0.5322624319280e+01, 0.1375773836557e+01,
6967
6968		0.4417005920067e-07, 0.6240817359284e+01, 0.2770348281756e+00,
6969		0.4686806749936e-07, 0.3214977301156e+01, 0.1143987543936e+00,
6970		0.3758892132305e-07, 0.5879809634765e+01, 0.1596186371003e+01,
6971		0.5151351332319e-07, 0.2893377688007e+00, 0.2228608264996e+00,
6972		0.4554683578572e-07, 0.5475427144122e+01, 0.1465949902372e+00,
6973		0.3442381385338e-07, 0.5992034796640e+01, 0.5070101000000e-01,
6974		0.2831093954933e-07, 0.5367350273914e+01, 0.3092784376656e+00,
6975		0.3756267090084e-07, 0.5758171285420e+01, 0.4903339079539e+00,
6976		0.2816374679892e-07, 0.1863718700923e+01, 0.2991266627620e+00,
6977		0.3419307025569e-07, 0.9524347534130e+00, 0.3518164938661e+00,
6978
6979		0.2904250494239e-07, 0.5304471615602e+01, 0.1099462426779e+00,
6980		0.2471734511206e-07, 0.1297069793530e+01, 0.6256703299991e+00,
6981		0.2539620831872e-07, 0.3281126083375e+01, 0.1256615170089e+02,
6982		0.2281017868007e-07, 0.1829122133165e+01, 0.6681224869435e+01,
6983		0.2275319473335e-07, 0.5797198160181e+01, 0.3932462625300e-02,
6984		0.2547755368442e-07, 0.4752697708330e+01, 0.1169588211447e+01,
6985		0.2285979669317e-07, 0.1223205292886e+01, 0.1045155034888e+01,
6986		0.1913386560994e-07, 0.1757532993389e+01, 0.1155361302111e+01,
6987		0.1809020525147e-07, 0.4246116108791e+01, 0.3368040641550e-01,
6988		0.1649213300201e-07, 0.1445162890627e+01, 0.4408250688924e+00,
6989
6990		0.1834972793932e-07, 0.1126917567225e+01, 0.4452511715700e-02,
6991		0.1439550648138e-07, 0.6160756834764e+01, 0.9420622223326e+00,
6992		0.1487645457041e-07, 0.4358761931792e+01, 0.4123712502208e+00,
6993		0.1731729516660e-07, 0.6134456753344e+01, 0.2108507877249e+00,
6994		0.1717747163567e-07, 0.1898186084455e+01, 0.2157473718317e+00,
6995		0.1418190430374e-07, 0.4180286741266e+01, 0.6521991896920e-01,
6996		0.1404844134873e-07, 0.7654053565412e-01, 0.4258542984690e-01,
6997		0.1409842846538e-07, 0.4418612420312e+01, 0.2258291676434e+00,
6998		0.1090948346291e-07, 0.1260615686131e+01, 0.4226656969313e+00,
6999		0.1357577323612e-07, 0.3558248818690e+01, 0.7923417740620e-01,
7000
7001		0.1018154061960e-07, 0.5676087241256e+01, 0.1456308687557e+00,
7002		0.1412073972109e-07, 0.8394392632422e+00, 0.1525316725248e+00,
7003		0.1030938326496e-07, 0.1653593274064e+01, 0.1795258541446e+01,
7004		0.1180081567104e-07, 0.1285802592036e+01, 0.7032915397480e-01,
7005		0.9708510575650e-08, 0.7631889488106e+00, 0.8434341241180e-01,
7006		0.9637689663447e-08, 0.4630642649176e+01, 0.1272681024002e+01,
7007		0.1068910429389e-07, 0.5294934032165e+01, 0.2123349582968e+00,
7008		0.1063716179336e-07, 0.2736266800832e+01, 0.2142632012598e+00,
7009		0.1234858713814e-07, 0.1302891146570e+01, 0.1847279083684e+00,
7010		0.8912631189738e-08, 0.3570415993621e+01, 0.2648454860559e+01,
7011
7012		0.1036378285534e-07, 0.4236693440949e+01, 0.1370332435159e+00,
7013		0.9667798501561e-08, 0.2960768892398e+01, 0.4376440768498e+00,
7014		0.8108314201902e-08, 0.6987781646841e+00, 0.2880807454688e+00,
7015		0.7648364324628e-08, 0.2499017863863e+01, 0.2037373330570e+00,
7016		0.7286136828406e-08, 0.3787426951665e+01, 0.1129145838217e+00,
7017		0.9448237743913e-08, 0.2694354332983e+01, 0.5272426800584e+00,
7018		0.9374276106428e-08, 0.4787121277064e+01, 0.5321392641652e+00,
7019		0.7100226287462e-08, 0.3530238792101e+00, 0.6288513220417e+00,
7020		0.9253056659571e-08, 0.1399478925664e+01, 0.1606092486742e+00,
7021		0.6636432145504e-08, 0.3479575438447e+01, 0.1368660381889e+01,
7022
7023		0.6469975312932e-08, 0.1383669964800e+01, 0.2008557621224e+01,
7024		0.7335849729765e-08, 0.1243698166898e+01, 0.9561746721300e-02,
7025		0.8743421205855e-08, 0.3776164289301e+01, 0.3801276407308e+00,
7026		0.5993635744494e-08, 0.5627122113596e+01, 0.2042657109477e+02,
7027		0.5981008479693e-08, 0.1674336636752e+01, 0.2111650433779e+01,
7028		0.6188535145838e-08, 0.5214925208672e+01, 0.4305306221819e+00,
7029		0.6596074017566e-08, 0.2907653268124e+01, 0.1063314406849e+01,
7030		0.6630815126226e-08, 0.2127643669658e+01, 0.8389694097774e+00,
7031		0.6156772830040e-08, 0.5082160803295e+01, 0.4234171675140e+00,
7032		0.6446960563014e-08, 0.1872100916905e+01, 0.5287268506303e+00,
7033
7034		0.6429324424668e-08, 0.5610276103577e+01, 0.5306550935933e+00,
7035		0.6302232396465e-08, 0.1592152049607e+01, 0.1253008786510e-01,
7036		0.6399244436159e-08, 0.2746214421532e+01, 0.5217580628120e+02,
7037		0.5474965172558e-08, 0.2317666374383e+01, 0.2221856701002e+01,
7038		0.5339293190692e-08, 0.1084724961156e+01, 0.7466759693650e-01,
7039		0.5334733683389e-08, 0.3594106067745e+01, 0.7489573444450e-01,
7040		0.5392665782110e-08, 0.5630254365606e+01, 0.1055449481598e+01,
7041		0.6682075673789e-08, 0.1518480041732e+01, 0.2213766559277e+00,
7042		0.5079130495960e-08, 0.2739765115711e+01, 0.2132517061319e+00,
7043		0.5077759793261e-08, 0.5290711290094e+01, 0.2133464534247e+00,
7044
7045		0.4832037368310e-08, 0.1404473217200e+01, 0.7160067364790e-01,
7046		0.6463279674802e-08, 0.6038381695210e+01, 0.2209183458640e-01,
7047		0.6240592771560e-08, 0.1290170653666e+01, 0.3306188016693e+00,
7048		0.4672013521493e-08, 0.3261895939677e+01, 0.7796265773310e-01,
7049		0.6500650750348e-08, 0.1154522312095e+01, 0.3884652414254e+00,
7050		0.6344161389053e-08, 0.6206111545062e+01, 0.7605151500000e-01,
7051		0.4682518370646e-08, 0.5409118796685e+01, 0.1073608853559e+01,
7052		0.5329460015591e-08, 0.1202985784864e+01, 0.7287631425543e+00,
7053		0.5701588675898e-08, 0.4098715257064e+01, 0.8731175355560e-01,
7054		0.6030690867211e-08, 0.4132033218460e+00, 0.9846002785331e+00,
7055
7056		0.4336256312655e-08, 0.1211415991827e+01, 0.4297791515992e+00,
7057		0.4688498808975e-08, 0.3765479072409e+01, 0.2127790306879e+00,
7058		0.4675578609335e-08, 0.4265540037226e+01, 0.2138191288687e+00,
7059		0.4225578112158e-08, 0.5237566010676e+01, 0.3407705765729e+00,
7060		0.5139422230028e-08, 0.1507173079513e+01, 0.7233337363710e-01,
7061		0.4619995093571e-08, 0.9023957449848e-01, 0.8603097737811e+00,
7062		0.4494776255461e-08, 0.5414930552139e+00, 0.7381754420900e-01,
7063		0.4274026276788e-08, 0.4145735303659e+01, 0.7574578717200e-01,
7064		0.5018141789353e-08, 0.3344408829055e+01, 0.3180992042600e-02,
7065		0.4866163952181e-08, 0.3348534657607e+01, 0.7722995774390e-01,
7066
7067		0.4111986020501e-08, 0.4198823597220e+00, 0.1451108196653e+00,
7068		0.3356142784950e-08, 0.5609144747180e+01, 0.1274714967946e+00,
7069		0.4070575554551e-08, 0.7028411059224e+00, 0.3503323232942e+00,
7070		0.3257451857278e-08, 0.5624697983086e+01, 0.5296435984654e+00,
7071		0.3256973703026e-08, 0.1857842076707e+01, 0.5297383457582e+00,
7072		0.3830771508640e-08, 0.4562887279931e+01, 0.9098186128426e+00,
7073		0.3725024005962e-08, 0.2358058692652e+00, 0.1084620721060e+00,
7074		0.3136763921756e-08, 0.2049731526845e+01, 0.2346394437820e+00,
7075		0.3795147256194e-08, 0.2432356296933e+00, 0.1862120789403e+00,
7076		0.2877342229911e-08, 0.5631101279387e+01, 0.1905464808669e+01,
7077
7078		0.3076931798805e-08, 0.1117615737392e+01, 0.3628624111593e+00,
7079		0.2734765945273e-08, 0.5899826516955e+01, 0.2131850110243e+00,
7080		0.2733405296885e-08, 0.2130562964070e+01, 0.2134131485323e+00,
7081		0.2898552353410e-08, 0.3462387048225e+00, 0.5291709230214e+00,
7082		0.2893736103681e-08, 0.8534352781543e+00, 0.5302110212022e+00,
7083		0.3095717734137e-08, 0.2875061429041e+01, 0.2976424921901e+00,
7084		0.2636190425832e-08, 0.2242512846659e+01, 0.1485980103780e+01,
7085		0.3645512095537e-08, 0.1354016903958e+01, 0.6044726378023e+00,
7086		0.2808173547723e-08, 0.6705114365631e-01, 0.6225157782540e-01,
7087		0.2625012866888e-08, 0.4775705748482e+01, 0.5268983110410e-01,
7088
7089		0.2572233995651e-08, 0.2638924216139e+01, 0.1258454114666e+01,
7090		0.2604238824792e-08, 0.4826358927373e+01, 0.2103781122809e+00,
7091		0.2596886385239e-08, 0.3200388483118e+01, 0.2162200472757e+00,
7092		0.3228057304264e-08, 0.5384848409563e+01, 0.2007689919132e+00,
7093		0.2481601798252e-08, 0.5173373487744e+01, 0.1062562936266e+01,
7094		0.2745977498864e-08, 0.6250966149853e+01, 0.5651155736444e+00,
7095		0.2669878833811e-08, 0.4906001352499e+01, 0.1400015846597e+00,
7096		0.3203986611711e-08, 0.5034333010005e+01, 0.7036329877322e+00,
7097		0.3354961227212e-08, 0.6108262423137e+01, 0.4549093064213e+00,
7098		0.2400407324558e-08, 0.2135399294955e+01, 0.2125476091956e+00,
7099
7100		0.2379905859802e-08, 0.5893721933961e+01, 0.2140505503610e+00,
7101		0.2550844302187e-08, 0.3331940762063e+01, 0.1534957940063e+00,
7102		0.2268824211001e-08, 0.1843418461035e+01, 0.2235935264888e+00,
7103		0.2464700891204e-08, 0.3029548547230e+01, 0.2091065926078e+00,
7104		0.2436814726024e-08, 0.4994717970364e+01, 0.2174915669488e+00,
7105		0.2443623894745e-08, 0.2645102591375e+01, 0.1739420156204e+00,
7106		0.2318701783838e-08, 0.5700547397897e+01, 0.7530171478090e-01,
7107		0.2284448700256e-08, 0.5268898905872e+01, 0.7426161660010e-01,
7108		0.2468848123510e-08, 0.5276280575078e+01, 0.2526561439362e+00,
7109		0.2814052350303e-08, 0.6130168623475e+01, 0.5636314030725e+00,
7110
7111		0.2243662755220e-08, 0.6631692457995e+00, 0.8886590321940e-01,
7112		0.2330795855941e-08, 0.2499435487702e+01, 0.1056200952181e+01,
7113		0.9757679038404e-09, 0.5796846023126e+01, 0.7826370942180e+02 };
7114
7115		/* SSB-to-Sun, T^0, Z */
7116	2	static final double s0z[] = {
7117		0.1181255122986e-03, 0.4607918989164e+00, 0.2132990797783e+00,
7118		0.1127777651095e-03, 0.4169146331296e+00, 0.5296909721118e+00,
7119		0.4777754401806e-04, 0.4582657007130e+01, 0.3813291813120e-01,
7120		0.1129354285772e-04, 0.5758735142480e+01, 0.7478166569050e-01,
7121		-0.1149543637123e-04, 0.0000000000000e+00, 0.0000000000000e+00,
7122		0.3298730512306e-05, 0.5978801994625e+01, 0.4265981595566e+00,
7123		0.2733376706079e-05, 0.7665413691040e+00, 0.1059381944224e+01,
7124		0.9426389657270e-06, 0.3710201265838e+01, 0.2061856251104e+00,
7125		0.8187517749552e-06, 0.3390675605802e+00, 0.2204125344462e+00,
7126		0.4080447871819e-06, 0.4552296640088e+00, 0.5225775174439e+00,
7127
7128		0.3169973017028e-06, 0.3445455899321e+01, 0.5368044267797e+00,
7129		0.2438098615549e-06, 0.5664675150648e+01, 0.3664874755930e-01,
7130		0.2601897517235e-06, 0.1931894095697e+01, 0.1495633313810e+00,
7131		0.2314558080079e-06, 0.3666319115574e+00, 0.3961708870310e-01,
7132		0.1962549548002e-06, 0.3167411699020e+01, 0.7626583626240e-01,
7133		0.2180518287925e-06, 0.1544420746580e+01, 0.7113454667900e-02,
7134		0.1451382442868e-06, 0.1583756740070e+01, 0.1102062672231e+00,
7135		0.1358439007389e-06, 0.5239941758280e+01, 0.6398972393349e+00,
7136		0.1050585898028e-06, 0.2266958352859e+01, 0.3163918923335e+00,
7137		0.1050029870186e-06, 0.2711495250354e+01, 0.4194847048887e+00,
7138
7139		0.9934920679800e-07, 0.1116208151396e+01, 0.1589072916335e+01,
7140		0.1048395331560e-06, 0.3408619600206e+01, 0.1021328554739e+02,
7141		0.8370147196668e-07, 0.3810459401087e+01, 0.2535050500000e-01,
7142		0.7989856510998e-07, 0.3769910473647e+01, 0.7329749511860e-01,
7143		0.5441221655233e-07, 0.2416994903374e+01, 0.1030928125552e+00,
7144		0.4610812906784e-07, 0.5858503336994e+01, 0.4337116142245e+00,
7145		0.3923022803444e-07, 0.3354170010125e+00, 0.1484170571900e-02,
7146		0.2610725582128e-07, 0.5410600646324e+01, 0.6327837846670e+00,
7147		0.2455279767721e-07, 0.6120216681403e+01, 0.1162474756779e+01,
7148		0.2375530706525e-07, 0.6055443426143e+01, 0.1052268489556e+01,
7149
7150		0.1782967577553e-07, 0.3146108708004e+01, 0.8460828644453e+00,
7151		0.1581687095238e-07, 0.6255496089819e+00, 0.3340612434717e+01,
7152		0.1594657672461e-07, 0.3782604300261e+01, 0.1066495398892e+01,
7153		0.1563448615040e-07, 0.1997775733196e+01, 0.2022531624851e+00,
7154		0.1463624258525e-07, 0.1736316792088e+00, 0.3516457698740e-01,
7155		0.1331585056673e-07, 0.4331941830747e+01, 0.9491756770005e+00,
7156		0.1130634557637e-07, 0.6152017751825e+01, 0.2968341143800e-02,
7157		0.1028949607145e-07, 0.2101792614637e+00, 0.2275259891141e+00,
7158		0.1024074971618e-07, 0.4071833211074e+01, 0.5070101000000e-01,
7159		0.8826956060303e-08, 0.4861633688145e+00, 0.2093666171530e+00,
7160
7161		0.8572230171541e-08, 0.5268190724302e+01, 0.4110125927500e-01,
7162		0.7649332643544e-08, 0.5134543417106e+01, 0.2608790314060e+02,
7163		0.8581673291033e-08, 0.2920218146681e+01, 0.1480791608091e+00,
7164		0.8430589300938e-08, 0.3604576619108e+01, 0.2172315424036e+00,
7165		0.7776165501012e-08, 0.3772942249792e+01, 0.6373574839730e-01,
7166		0.8311070234408e-08, 0.6200412329888e+01, 0.3235053470014e+00,
7167		0.6927365212582e-08, 0.4543353113437e+01, 0.8531963191132e+00,
7168		0.6791574208598e-08, 0.2882188406238e+01, 0.7181332454670e-01,
7169		0.5593100811839e-08, 0.1776646892780e+01, 0.7429900518901e+00,
7170		0.4553381853021e-08, 0.3949617611240e+01, 0.7775000683430e-01,
7171
7172		0.5758000450068e-08, 0.3859251775075e+01, 0.1990721704425e+00,
7173		0.4281283457133e-08, 0.1466294631206e+01, 0.2118763888447e+01,
7174		0.4206935661097e-08, 0.5421776011706e+01, 0.1104591729320e-01,
7175		0.4213751641837e-08, 0.3412048993322e+01, 0.2243449970715e+00,
7176		0.5310506239878e-08, 0.5421641370995e+00, 0.5154640627760e+00,
7177		0.3827450341320e-08, 0.8887314524995e+00, 0.1510475019529e+00,
7178		0.4292435241187e-08, 0.1405043757194e+01, 0.1422690933580e-01,
7179		0.3189780702289e-08, 0.1060049293445e+01, 0.1173197218910e+00,
7180		0.3226611928069e-08, 0.6270858897442e+01, 0.2164800718209e+00,
7181		0.2893897608830e-08, 0.5117563223301e+01, 0.6470106940028e+00,
7182
7183		0.3239852024578e-08, 0.4079092237983e+01, 0.2101180877357e+00,
7184		0.2956892222200e-08, 0.1594917021704e+01, 0.3092784376656e+00,
7185		0.2980177912437e-08, 0.5258787667564e+01, 0.4155522422634e+00,
7186		0.3163725690776e-08, 0.3854589225479e+01, 0.8582758298370e-01,
7187		0.2662262399118e-08, 0.3561326430187e+01, 0.5257585094865e+00,
7188		0.2766689135729e-08, 0.3180732086830e+00, 0.1385174140878e+00,
7189		0.2411600278464e-08, 0.3324798335058e+01, 0.5439178814476e+00,
7190		0.2483527695131e-08, 0.4169069291947e+00, 0.5336234347371e+00,
7191		0.7788777276590e-09, 0.1900569908215e+01, 0.5217580628120e+02 };
7192
7193		/* SSB-to-Sun, T^1, X */
7194	2	static final double s1x[] = {
7195		-0.1296310361520e-07, 0.0000000000000e+00, 0.0000000000000e+00,
7196		0.8975769009438e-08, 0.1128891609250e+01, 0.4265981595566e+00,
7197		0.7771113441307e-08, 0.2706039877077e+01, 0.2061856251104e+00,
7198		0.7538303866642e-08, 0.2191281289498e+01, 0.2204125344462e+00,
7199		0.6061384579336e-08, 0.3248167319958e+01, 0.1059381944224e+01,
7200		0.5726994235594e-08, 0.5569981398610e+01, 0.5225775174439e+00,
7201		0.5616492836424e-08, 0.5057386614909e+01, 0.5368044267797e+00,
7202		0.1010881584769e-08, 0.3473577116095e+01, 0.7113454667900e-02,
7203		0.7259606157626e-09, 0.3651858593665e+00, 0.6398972393349e+00,
7204		0.8755095026935e-09, 0.1662835408338e+01, 0.4194847048887e+00,
7205
7206		0.5370491182812e-09, 0.1327673878077e+01, 0.4337116142245e+00,
7207		0.5743773887665e-09, 0.4250200846687e+01, 0.2132990797783e+00,
7208		0.4408103140300e-09, 0.3598752574277e+01, 0.1589072916335e+01,
7209		0.3101892374445e-09, 0.4887822983319e+01, 0.1052268489556e+01,
7210		0.3209453713578e-09, 0.9702272295114e+00, 0.5296909721118e+00,
7211		0.3017228286064e-09, 0.5484462275949e+01, 0.1066495398892e+01,
7212		0.3200700038601e-09, 0.2846613338643e+01, 0.1495633313810e+00,
7213		0.2137637279911e-09, 0.5692163292729e+00, 0.3163918923335e+00,
7214		0.1899686386727e-09, 0.2061077157189e+01, 0.2275259891141e+00,
7215		0.1401994545308e-09, 0.4177771136967e+01, 0.1102062672231e+00,
7216
7217		0.1578057810499e-09, 0.5782460597335e+01, 0.7626583626240e-01,
7218		0.1237713253351e-09, 0.5705900866881e+01, 0.5154640627760e+00,
7219		0.1313076837395e-09, 0.5163438179576e+01, 0.3664874755930e-01,
7220		0.1184963304860e-09, 0.3054804427242e+01, 0.6327837846670e+00,
7221		0.1238130878565e-09, 0.2317292575962e+01, 0.3961708870310e-01,
7222		0.1015959527736e-09, 0.2194643645526e+01, 0.7329749511860e-01,
7223		0.9017954423714e-10, 0.2868603545435e+01, 0.1990721704425e+00,
7224		0.8668024955603e-10, 0.4923849675082e+01, 0.5439178814476e+00,
7225		0.7756083930103e-10, 0.3014334135200e+01, 0.9491756770005e+00,
7226		0.7536503401741e-10, 0.2704886279769e+01, 0.1030928125552e+00,
7227
7228		0.5483308679332e-10, 0.6010983673799e+01, 0.8531963191132e+00,
7229		0.5184339620428e-10, 0.1952704573291e+01, 0.2093666171530e+00,
7230		0.5108658712030e-10, 0.2958575786649e+01, 0.2172315424036e+00,
7231		0.5019424524650e-10, 0.1736317621318e+01, 0.2164800718209e+00,
7232		0.4909312625978e-10, 0.3167216416257e+01, 0.2101180877357e+00,
7233		0.4456638901107e-10, 0.7697579923471e+00, 0.3235053470014e+00,
7234		0.4227030350925e-10, 0.3490910137928e+01, 0.6373574839730e-01,
7235		0.4095456040093e-10, 0.5178888984491e+00, 0.6470106940028e+00,
7236		0.4990537041422e-10, 0.3323887668974e+01, 0.1422690933580e-01,
7237		0.4321170010845e-10, 0.4288484987118e+01, 0.7358765972222e+00,
7238
7239		0.3544072091802e-10, 0.6021051579251e+01, 0.5265099800692e+00,
7240		0.3480198638687e-10, 0.4600027054714e+01, 0.5328719641544e+00,
7241		0.3440287244435e-10, 0.4349525970742e+01, 0.8582758298370e-01,
7242		0.3330628322713e-10, 0.2347391505082e+01, 0.1104591729320e-01,
7243		0.2973060707184e-10, 0.4789409286400e+01, 0.5257585094865e+00,
7244		0.2932606766089e-10, 0.5831693799927e+01, 0.5336234347371e+00,
7245		0.2876972310953e-10, 0.2692638514771e+01, 0.1173197218910e+00,
7246		0.2827488278556e-10, 0.2056052487960e+01, 0.2022531624851e+00,
7247		0.2515028239756e-10, 0.7411863262449e+00, 0.9597935788730e-01,
7248		0.2853033744415e-10, 0.3948481024894e+01, 0.2118763888447e+01 };
7249
7250		/* SSB-to-Sun, T^1, Y */
7251	2	static final double s1y[] = {
7252		0.8989047573576e-08, 0.5840593672122e+01, 0.4265981595566e+00,
7253		0.7815938401048e-08, 0.1129664707133e+01, 0.2061856251104e+00,
7254		0.7550926713280e-08, 0.6196589104845e+00, 0.2204125344462e+00,
7255		0.6056556925895e-08, 0.1677494667846e+01, 0.1059381944224e+01,
7256		0.5734142698204e-08, 0.4000920852962e+01, 0.5225775174439e+00,
7257		0.5614341822459e-08, 0.3486722577328e+01, 0.5368044267797e+00,
7258		0.1028678147656e-08, 0.1877141024787e+01, 0.7113454667900e-02,
7259		0.7270792075266e-09, 0.5077167301739e+01, 0.6398972393349e+00,
7260		0.8734141726040e-09, 0.9069550282609e-01, 0.4194847048887e+00,
7261		0.5377371402113e-09, 0.6039381844671e+01, 0.4337116142245e+00,
7262
7263		0.4729719431571e-09, 0.2153086311760e+01, 0.2132990797783e+00,
7264		0.4458052820973e-09, 0.5059830025565e+01, 0.5296909721118e+00,
7265		0.4406855467908e-09, 0.2027971692630e+01, 0.1589072916335e+01,
7266		0.3101659310977e-09, 0.3317677981860e+01, 0.1052268489556e+01,
7267		0.3016749232545e-09, 0.3913703482532e+01, 0.1066495398892e+01,
7268		0.3198541352656e-09, 0.1275513098525e+01, 0.1495633313810e+00,
7269		0.2142065389871e-09, 0.5301351614597e+01, 0.3163918923335e+00,
7270		0.1902615247592e-09, 0.4894943352736e+00, 0.2275259891141e+00,
7271		0.1613410990871e-09, 0.2449891130437e+01, 0.1102062672231e+00,
7272		0.1576992165097e-09, 0.4211421447633e+01, 0.7626583626240e-01,
7273
7274		0.1241637259894e-09, 0.4140803368133e+01, 0.5154640627760e+00,
7275		0.1313974830355e-09, 0.3591920305503e+01, 0.3664874755930e-01,
7276		0.1181697118258e-09, 0.1506314382788e+01, 0.6327837846670e+00,
7277		0.1238239742779e-09, 0.7461405378404e+00, 0.3961708870310e-01,
7278		0.1010107068241e-09, 0.6271010795475e+00, 0.7329749511860e-01,
7279		0.9226316616509e-10, 0.1259158839583e+01, 0.1990721704425e+00,
7280		0.8664946419555e-10, 0.3353244696934e+01, 0.5439178814476e+00,
7281		0.7757230468978e-10, 0.1447677295196e+01, 0.9491756770005e+00,
7282		0.7693168628139e-10, 0.1120509896721e+01, 0.1030928125552e+00,
7283		0.5487897454612e-10, 0.4439380426795e+01, 0.8531963191132e+00,
7284
7285		0.5196118677218e-10, 0.3788856619137e+00, 0.2093666171530e+00,
7286		0.5110853339935e-10, 0.1386879372016e+01, 0.2172315424036e+00,
7287		0.5027804534813e-10, 0.1647881805466e+00, 0.2164800718209e+00,
7288		0.4922485922674e-10, 0.1594315079862e+01, 0.2101180877357e+00,
7289		0.6155599524400e-10, 0.0000000000000e+00, 0.0000000000000e+00,
7290		0.4447147832161e-10, 0.5480720918976e+01, 0.3235053470014e+00,
7291		0.4144691276422e-10, 0.1931371033660e+01, 0.6373574839730e-01,
7292		0.4099950625452e-10, 0.5229611294335e+01, 0.6470106940028e+00,
7293		0.5060541682953e-10, 0.1731112486298e+01, 0.1422690933580e-01,
7294		0.4293615946300e-10, 0.2714571038925e+01, 0.7358765972222e+00,
7295
7296		0.3545659845763e-10, 0.4451041444634e+01, 0.5265099800692e+00,
7297		0.3479112041196e-10, 0.3029385448081e+01, 0.5328719641544e+00,
7298		0.3438516493570e-10, 0.2778507143731e+01, 0.8582758298370e-01,
7299		0.3297341285033e-10, 0.7898709807584e+00, 0.1104591729320e-01,
7300		0.2972585818015e-10, 0.3218785316973e+01, 0.5257585094865e+00,
7301		0.2931707295017e-10, 0.4260731012098e+01, 0.5336234347371e+00,
7302		0.2897198149403e-10, 0.1120753978101e+01, 0.1173197218910e+00,
7303		0.2832293240878e-10, 0.4597682717827e+00, 0.2022531624851e+00,
7304		0.2864348326612e-10, 0.2169939928448e+01, 0.9597935788730e-01,
7305		0.2852714675471e-10, 0.2377659870578e+01, 0.2118763888447e+01 };
7306
7307		/* SSB-to-Sun, T^1, Z */
7308	2	static final double s1z[] = {
7309		0.5444220475678e-08, 0.1803825509310e+01, 0.2132990797783e+00,
7310		0.3883412695596e-08, 0.4668616389392e+01, 0.5296909721118e+00,
7311		0.1334341434551e-08, 0.0000000000000e+00, 0.0000000000000e+00,
7312		0.3730001266883e-09, 0.5401405918943e+01, 0.2061856251104e+00,
7313		0.2894929197956e-09, 0.4932415609852e+01, 0.2204125344462e+00,
7314		0.2857950357701e-09, 0.3154625362131e+01, 0.7478166569050e-01,
7315		0.2499226432292e-09, 0.3657486128988e+01, 0.4265981595566e+00,
7316		0.1937705443593e-09, 0.5740434679002e+01, 0.1059381944224e+01,
7317		0.1374894396320e-09, 0.1712857366891e+01, 0.5368044267797e+00,
7318		0.1217248678408e-09, 0.2312090870932e+01, 0.5225775174439e+00,
7319
7320		0.7961052740870e-10, 0.5283368554163e+01, 0.3813291813120e-01,
7321		0.4979225949689e-10, 0.4298290471860e+01, 0.4194847048887e+00,
7322		0.4388552286597e-10, 0.6145515047406e+01, 0.7113454667900e-02,
7323		0.2586835212560e-10, 0.3019448001809e+01, 0.6398972393349e+00 };
7324
7325		/* SSB-to-Sun, T^2, X */
7326	2	static final double s2x[] = {
7327		0.1603551636587e-11, 0.4404109410481e+01, 0.2061856251104e+00,
7328		0.1556935889384e-11, 0.4818040873603e+00, 0.2204125344462e+00,
7329		0.1182594414915e-11, 0.9935762734472e+00, 0.5225775174439e+00,
7330		0.1158794583180e-11, 0.3353180966450e+01, 0.5368044267797e+00,
7331		0.9597358943932e-12, 0.5567045358298e+01, 0.2132990797783e+00,
7332		0.6511516579605e-12, 0.5630872420788e+01, 0.4265981595566e+00,
7333		0.7419792747688e-12, 0.2156188581957e+01, 0.5296909721118e+00,
7334		0.3951972655848e-12, 0.1981022541805e+01, 0.1059381944224e+01,
7335		0.4478223877045e-12, 0.0000000000000e+00, 0.0000000000000e+00 };
7336
7337		/* SSB-to-Sun, T^2, Y */
7338	2	static final double s2y[] = {
7339		0.1609114495091e-11, 0.2831096993481e+01, 0.2061856251104e+00,
7340		0.1560330784946e-11, 0.5193058213906e+01, 0.2204125344462e+00,
7341		0.1183535479202e-11, 0.5707003443890e+01, 0.5225775174439e+00,
7342		0.1158183066182e-11, 0.1782400404928e+01, 0.5368044267797e+00,
7343		0.1032868027407e-11, 0.4036925452011e+01, 0.2132990797783e+00,
7344		0.6540142847741e-12, 0.4058241056717e+01, 0.4265981595566e+00,
7345		0.7305236491596e-12, 0.6175401942957e+00, 0.5296909721118e+00,
7346		-0.5580725052968e-12, 0.0000000000000e+00, 0.0000000000000e+00,
7347		0.3946122651015e-12, 0.4108265279171e+00, 0.1059381944224e+01 };
7348
7349		/* SSB-to-Sun, T^2, Z */
7350	2	static final double s2z[] = {
7351		0.3749920358054e-12, 0.3230285558668e+01, 0.2132990797783e+00,
7352		0.2735037220939e-12, 0.6154322683046e+01, 0.5296909721118e+00 };
7353		}
7354
7355		/**
7356		* Earth position and velocity, heliocentric and barycentric, with
7357		* respect to the Barycentric Celestial Reference System.
7358		*
7359		*<p>This function is derived from the International Astronomical Union's
7360		* SOFA (Standards Of Fundamental Astronomy) software collection.
7361		*
7362		*<p>Status: support function.
7363		*
7364		*<!-- Given: -->
7365		* @param date1 double TDB date (Note 1)
7366		* @param date2 double TDB date (Note 1)
7367		*
7368		*<!-- Returned: -->
7369		* @param pvh double[2][3] <u>returned</u> heliocentric Earth position/velocity (AU, AU/d)
7370		* @param pvb double[2][3] <u>returned</u> barycentric Earth position/velocity (AU, AU/d)
7371		*
7372		* <!-- Returned (function value): -->
7373		* @return int status: 0 = OK
7374		* +1 = warning: date outside
7375		* the range 1900-2100 AD
7376		*
7377		* <p>Notes:
7378		* <ol>
7379		*
7380		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
7381		* convenient way between the two arguments. For example,
7382		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
7383		* others:
7384		*<pre>
7385		* date1 date2
7386		*
7387		* 2450123.7 0.0 (JD method)
7388		* 2451545.0 -1421.3 (J2000 method)
7389		* 2400000.5 50123.2 (MJD method)
7390		* 2450123.5 0.2 (date & time method)
7391		*</pre>
7392		* The JD method is the most natural and convenient to use in cases
7393		* where the loss of several decimal digits of resolution is
7394		* acceptable. The J2000 method is best matched to the way the
7395		* argument is handled internally and will deliver the optimum
7396		* resolution. The MJD method and the date & time methods are both
7397		* good compromises between resolution and convenience. However,
7398		* the accuracy of the result is more likely to be limited by the
7399		* algorithm itself than the way the date has been expressed.
7400		*
7401		* n.b. TT can be used instead of TDB in most applications.
7402		*
7403		* <li> On return, the arrays pvh and pvb contain the following:
7404		*
7405		* pvh[0][0] x }
7406		* pvh[0][1] y } heliocentric position, AU
7407		* pvh[0][2] z }
7408		*
7409		* pvh[1][0] xdot }
7410		* pvh[1][1] ydot } heliocentric velocity, AU/d
7411		* pvh[1][2] zdot }
7412		*
7413		* pvb[0][0] x }
7414		* pvb[0][1] y } barycentric position, AU
7415		* pvb[0][2] z }
7416		*
7417		* pvb[1][0] xdot }
7418		* pvb[1][1] ydot } barycentric velocity, AU/d
7419		* pvb[1][2] zdot }
7420		*
7421		* The vectors are with respect to the Barycentric Celestial
7422		* Reference System. The time unit is one day in TDB.
7423		*
7424		* <li> The function is a SIMPLIFIED SOLUTION from the planetary theory
7425		* VSOP2000 (X. Moisson, P. Bretagnon, 2001, Celes. Mechanics &
7426		* Dyn. Astron., 80, 3/4, 205-213) and is an adaptation of original
7427		* Fortran code supplied by P. Bretagnon (private comm., 2000).
7428		*
7429		* <li> Comparisons over the time span 1900-2100 with this simplified
7430		* solution and the JPL DE405 ephemeris give the following results:
7431		*
7432		* RMS max
7433		* Heliocentric:
7434		* position error 3.7 11.2 km
7435		* velocity error 1.4 5.0 mm/s
7436		*
7437		* Barycentric:
7438		* position error 4.6 13.4 km
7439		* velocity error 1.4 4.9 mm/s
7440		*
7441		* Comparisons with the JPL DE406 ephemeris show that by 1800 and
7442		* 2200 the position errors are approximately double their 1900-2100
7443		* size. By 1500 and 2500 the deterioration is a factor of 10 and
7444		* by 1000 and 3000 a factor of 60. The velocity accuracy falls off
7445		* at about half that rate.
7446		*
7447		* <li> It is permissible to use the same array for pvh and pvb, which
7448		* will receive the barycentric values.
7449		*</ol>
7450		*@version 2008 November 18
7451		*
7452		* @since Release 20101201
7453		*
7454		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7455		*/
7456		public static int jauEpv00(final double date1, final double date2,
7457		double pvh[][], double pvb[][])
7458		{
7459		/*
7460		* Matrix elements for orienting the analytical model to DE405.
7461		*
7462		* The corresponding Euler angles are:
7463		*
7464		* d ' "
7465		* 1st rotation - 23 26 21.4091 about the x-axis (obliquity)
7466		* 2nd rotation + 0.0475 about the z-axis (RA offset)
7467		*
7468		* These were obtained empirically, by comparisons with DE405 over
7469		* 1900-2100.
7470		*/
7471	32	final double am12 = 0.000000211284,
7472	32	am13 = -0.000000091603,
7473	32	am21 = -0.000000230286,
7474	32	am22 = 0.917482137087,
7475	32	am23 = -0.397776982902,
7476	32	am32 = 0.397776982902,
7477	32	am33 = 0.917482137087;
7478
7479
7480
7481
7482		/* Pointers to coefficient arrays, in x,y,z sets */
7483	32	final double ce0[][] = { Ephemeris.e0x, Ephemeris.e0y, Ephemeris.e0z },
7484	32	ce1[][] = { Ephemeris.e1x, Ephemeris.e1y, Ephemeris.e1z },
7485	32	ce2[][] = { Ephemeris.e2x, Ephemeris.e2y, Ephemeris.e2z },
7486	32	cs0[][] = { Ephemeris.s0x, Ephemeris.s0y, Ephemeris.s0z },
7487	32	cs1[][] = { Ephemeris.s1x, Ephemeris.s1y, Ephemeris.s1z },
7488	32	cs2[][] = { Ephemeris.s2x, Ephemeris.s2y, Ephemeris.s2z };
7489		/* Numbers of terms for each component of the model, in x,y,z sets */
7490	32	final int ne0[] = {Ephemeris.e0x.length/3,
7491		Ephemeris.e0y.length/3,
7492		Ephemeris.e0z.length/3 },
7493	32	ne1[] = {Ephemeris.e1x.length/3,
7494		Ephemeris.e1y.length/3,
7495		Ephemeris.e1z.length/3 },
7496	32	ne2[] = {Ephemeris.e2x.length/3,
7497		Ephemeris.e2y.length/3,
7498		Ephemeris.e2z.length/3 },
7499	32	ns0[] = {Ephemeris.s0x.length/3,
7500		Ephemeris.s0y.length/3,
7501		Ephemeris.s0z.length/3 },
7502	32	ns1[] = {Ephemeris.s1x.length/3,
7503		Ephemeris.s1y.length/3,
7504		Ephemeris.s1z.length/3 },
7505	32	ns2[] = {Ephemeris.s2x.length/3,
7506		Ephemeris.s2y.length/3,
7507		Ephemeris.s2z.length/3 };
7508		int nterms;
7509
7510		/* Miscellaneous */
7511		int jstat, i, j;
7512		double t, t2, xyz, xyzd, a, b, c, ct, p, cp,
7513	32	ph[] = new double[3], vh[] = new double[3], pb[] = new double[3], vb[] = new double[3], x, y, z;
7514
7515		/--------------------------------------------------------------------/
7516
7517		/* Time since reference epoch, Julian years. */
7518	32	t = ((date1 - DJ00) + date2) / DJY;
7519	32	t2 = t*t;
7520
7521		/* Set status. */
7522	32	jstat = abs(t) <= 100.0 ? 0 : 1;
7523
7524		/* X then Y then Z. */
7525	128	for (i = 0; i < 3; i++) {
7526
7527		/* Initialize position and velocity component. */
7528	96	xyz = 0.0;
7529	96	xyzd = 0.0;
7530
7531		/* ------------------------------------------------ */
7532		/* Obtain component of Sun to Earth ecliptic vector */
7533		/* ------------------------------------------------ */
7534
7535		/* Sun to Earth, T^0 terms. */
7536	96	nterms = ne0[i];
7537		int idx;
7538	36544	for (j = 0, idx=0; j < nterms; j++) {
7539	36448	a = ce0[i][idx++];
7540	36448	b = ce0[i][idx++];
7541	36448	c = ce0[i][idx++];
7542	36448	p = b + c*t;
7543	36448	xyz += a*cos(p);
7544	36448	xyzd -= acsin(p);
7545		}
7546
7547		/* Sun to Earth, T^1 terms. */
7548	96	nterms = ne1[i];
7549	5568	for (j = 0, idx= 0; j < nterms; j++) {
7550	5472	a = ce1[i][idx++];
7551	5472	b = ce1[i][idx++];
7552	5472	c = ce1[i][idx++];
7553	5472	ct = c*t;
7554	5472	p = b + ct;
7555	5472	cp = cos(p);
7556	5472	xyz += atcp;
7557	5472	xyzd += a( cp - ctsin(p) );
7558		}
7559
7560		/* Sun to Earth, T^2 terms. */
7561	96	nterms = ne2[i];
7562	512	for (j = 0, idx = 0; j < nterms; j++) {
7563	416	a = ce2[i][idx++];
7564	416	b = ce2[i][idx++];
7565	416	c = ce2[i][idx++];
7566	416	ct = c*t;
7567	416	p = b + ct;
7568	416	cp = cos(p);
7569	416	xyz += at2cp;
7570	416	xyzd += at( 2.0cp - ctsin(p) );
7571		}
7572
7573		/* Heliocentric Earth position and velocity component. */
7574	96	ph[i] = xyz;
7575	96	vh[i] = xyzd / DJY;
7576
7577		/* ------------------------------------------------ */
7578		/* Obtain component of SSB to Earth ecliptic vector */
7579		/* ------------------------------------------------ */
7580
7581		/* SSB to Sun, T^0 terms. */
7582	96	nterms = ns0[i];
7583	15904	for (j = 0, idx = 0; j < nterms; j++) {
7584	15808	a = cs0[i][idx++];
7585	15808	b = cs0[i][idx++];
7586	15808	c = cs0[i][idx++];
7587	15808	p = b + c*t;
7588	15808	xyz += a*cos(p);
7589	15808	xyzd -= acsin(p);
7590		}
7591
7592		/* SSB to Sun, T^1 terms. */
7593	96	nterms = ns1[i];
7594	3744	for (j = 0, idx = 0; j < nterms; j++) {
7595	3648	a = cs1[i][idx++];
7596	3648	b = cs1[i][idx++];
7597	3648	c = cs1[i][idx++];
7598	3648	ct = c*t;
7599	3648	p = b + ct;
7600	3648	cp = cos(p);
7601	3648	xyz += atcp;
7602	3648	xyzd += a(cp - ctsin(p));
7603		}
7604
7605		/* SSB to Sun, T^2 terms. */
7606	96	nterms = ns2[i];
7607	736	for (j = 0, idx = 0; j < nterms; j++) {
7608	640	a = cs2[i][idx++];
7609	640	b = cs2[i][idx++];
7610	640	c = cs2[i][idx++];
7611	640	ct = c*t;
7612	640	p = b + ct;
7613	640	cp = cos(p);
7614	640	xyz += at2cp;
7615	640	xyzd += at(2.0cp - ctsin(p));
7616		}
7617
7618		/* Barycentric Earth position and velocity component. */
7619	96	pb[i] = xyz;
7620	96	vb[i] = xyzd / DJY;
7621
7622		/* Next Cartesian component. */
7623		}
7624
7625		/* Rotate from ecliptic to BCRS coordinates. */
7626
7627	32	x = ph[0];
7628	32	y = ph[1];
7629	32	z = ph[2];
7630	32	pvh[0][0] = x + am12y + am13z;
7631	32	pvh[0][1] = am21x + am22y + am23*z;
7632	32	pvh[0][2] = am32y + am33z;
7633
7634	32	x = vh[0];
7635	32	y = vh[1];
7636	32	z = vh[2];
7637	32	pvh[1][0] = x + am12y + am13z;
7638	32	pvh[1][1] = am21x + am22y + am23*z;
7639	32	pvh[1][2] = am32y + am33z;
7640
7641	32	x = pb[0];
7642	32	y = pb[1];
7643	32	z = pb[2];
7644	32	pvb[0][0] = x + am12y + am13z;
7645	32	pvb[0][1] = am21x + am22y + am23*z;
7646	32	pvb[0][2] = am32y + am33z;
7647
7648	32	x = vb[0];
7649	32	y = vb[1];
7650	32	z = vb[2];
7651	32	pvb[1][0] = x + am12y + am13z;
7652	32	pvb[1][1] = am21x + am22y + am23*z;
7653	32	pvb[1][2] = am32y + am33z;
7654
7655		/* Return the status. */
7656	32	return jstat;
7657
7658		}
7659
7660
7661		/**
7662		* Equation of the equinoxes, IAU 1994 model.
7663		*
7664		*<p>This function is derived from the International Astronomical Union's
7665		* SOFA (Standards Of Fundamental Astronomy) software collection.
7666		*
7667		*<p>Status: canonical model.
7668		*
7669		*<!-- Given: -->
7670		* @param date1 double TDB date (Note 1)
7671		* @param date2 double TDB date (Note 1)
7672		*
7673		* <!-- Returned (function value): -->
7674		* @return double equation of the equinoxes (Note 2)
7675		*
7676		* <p>Notes:
7677		* <ol>
7678		*
7679		* <li> The date date1+date2 is a Julian Date, apportioned in any
7680		* convenient way between the two arguments. For example,
7681		* JD(TT)=2450123.7 could be expressed in any of these ways,
7682		* among others:
7683		*<pre>
7684		* date1 date2
7685		*
7686		* 2450123.7 0.0 (JD method)
7687		* 2451545.0 -1421.3 (J2000 method)
7688		* 2400000.5 50123.2 (MJD method)
7689		* 2450123.5 0.2 (date & time method)
7690		*</pre>
7691		* The JD method is the most natural and convenient to use in
7692		* cases where the loss of several decimal digits of resolution
7693		* is acceptable. The J2000 method is best matched to the way
7694		* the argument is handled internally and will deliver the
7695		* optimum resolution. The MJD method and the date & time methods
7696		* are both good compromises between resolution and convenience.
7697		*
7698		* <li> The result, which is in radians, operates in the following sense:
7699		*
7700		* Greenwich apparent ST = GMST + equation of the equinoxes
7701		*</ol>
7702		*<p>Called:<ul>
7703		* <li>{@link #jauNut80} nutation, IAU 1980
7704		* <li>{@link #jauObl80} mean obliquity, IAU 1980
7705		* </ul>
7706		*<p>References:
7707		*
7708		* <p>IAU Resolution C7, Recommendation 3 (1994).
7709		*
7710		* <p>Capitaine, N. & Gontier, A.-M., 1993, Astron. Astrophys., 275,
7711		* 645-650.
7712		*
7713		*@version 2008 May 24
7714		*
7715		* @since Release 20101201
7716		*
7717		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7718		*/
7719		public static double jauEqeq94(double date1, double date2)
7720		{
7721		double t, om, eps0, ee;
7722
7723
7724		/* Interval between fundamental epoch J2000.0 and given date (JC). */
7725	4	t = ((date1 - DJ00) + date2) / DJC;
7726
7727		/* Longitude of the mean ascending node of the lunar orbit on the */
7728		/* ecliptic, measured from the mean equinox of date. */
7729	8	om = jauAnpm((450160.280 + (-482890.539
7730		+ (7.455 + 0.008 * t) * t) * t) * DAS2R
7731	4	+ fmod(-5.0 * t, 1.0) * D2PI);
7732
7733		/* Nutation components and mean obliquity. */
7734	4	NutationTerms nt = jauNut80(date1, date2);
7735	4	eps0 = jauObl80(date1, date2);
7736
7737		/* Equation of the equinoxes. */
7738	4	ee = nt.dpsicos(eps0) + DAS2R(0.00264sin(om) + 0.000063sin(om+om));
7739
7740	4	return ee;
7741
7742		}
7743
7744
7745		/**
7746		* Earth rotation angle (IAU 2000 model).
7747		*
7748		*<p>This function is derived from the International Astronomical Union's
7749		* SOFA (Standards Of Fundamental Astronomy) software collection.
7750		*
7751		*<p>Status: canonical model.
7752		*
7753		*<!-- Given: -->
7754		* @param dj1 double UT1 as a 2-part Julian Date (see note)
7755		* @param dj2 double UT1 as a 2-part Julian Date (see note)
7756		*
7757		* <!-- Returned (function value): -->
7758		* @return double Earth rotation angle (radians), range 0-2pi
7759		*
7760		* <p>Notes:
7761		* <ol>
7762		*
7763		* <li> The UT1 date dj1+dj2 is a Julian Date, apportioned in any
7764		* convenient way between the arguments dj1 and dj2. For example,
7765		* JD(UT1)=2450123.7 could be expressed in any of these ways,
7766		* among others:
7767		*<pre>
7768		* dj1 dj2
7769		*
7770		* 2450123.7 0.0 (JD method)
7771		* 2451545.0 -1421.3 (J2000 method)
7772		* 2400000.5 50123.2 (MJD method)
7773		* 2450123.5 0.2 (date & time method)
7774		*</pre>
7775		* The JD method is the most natural and convenient to use in
7776		* cases where the loss of several decimal digits of resolution
7777		* is acceptable. The J2000 and MJD methods are good compromises
7778		* between resolution and convenience. The date & time method is
7779		* best matched to the algorithm used: maximum precision is
7780		* delivered when the dj1 argument is for 0hrs UT1 on the day in
7781		* question and the dj2 argument lies in the range 0 to 1, or vice
7782		* versa.
7783		*
7784		* <li> The algorithm is adapted from Expression 22 of Capitaine et al.
7785		* 2000. The time argument has been expressed in days directly,
7786		* and, to retain precision, integer contributions have been
7787		* eliminated. The same formulation is given in IERS Conventions
7788		* (2003), Chap. 5, Eq. 14.
7789		*</ol>
7790		*<p>Called:<ul>
7791		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
7792		* </ul>
7793		*<p>References:
7794		*
7795		* <p>Capitaine N., Guinot B. and McCarthy D.D, 2000, Astron.
7796		* Astrophys., 355, 398-405.
7797		*
7798		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7799		* IERS Technical Note No. 32, BKG (2004)
7800		*
7801		*@version 2008 May 24
7802		*
7803		* @since Release 20101201
7804		*
7805		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7806		*/
7807		public static double jauEra00(double dj1, double dj2)
7808		{
7809		double d1, d2, t, f, theta;
7810
7811
7812		/* Days since fundamental epoch. */
7813	54	if (dj1 < dj2) {
7814	0	d1 = dj1;
7815	0	d2 = dj2;
7816		} else {
7817	54	d1 = dj2;
7818	54	d2 = dj1;
7819		}
7820	54	t = d1 + (d2- DJ00);
7821
7822		/* Fractional part of T (days). */
7823	54	f = fmod(d1, 1.0) + fmod(d2, 1.0);
7824
7825		/* Earth rotation angle at this UT1. */
7826	54	theta = jauAnp(D2PI * (f + 0.7790572732640
7827		+ 0.00273781191135448 * t));
7828
7829	54	return theta;
7830
7831		}
7832
7833
7834		/**
7835		* Fundamental argument, IERS Conventions (2003):
7836		* mean elongation of the Moon from the Sun.
7837		*
7838		*<p>This function is derived from the International Astronomical Union's
7839		* SOFA (Standards Of Fundamental Astronomy) software collection.
7840		*
7841		*<p>Status: canonical model.
7842		*
7843		*<!-- Given: -->
7844		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
7845		*
7846		* <!-- Returned (function value): -->
7847		* @return double D, radians (Note 2)
7848		*
7849		* <p>Notes:
7850		* <ol>
7851		*
7852		* <li> Though t is strictly TDB, it is usually more convenient to use
7853		* TT, which makes no significant difference.
7854		*
7855		* <li> The expression used is as adopted in IERS Conventions (2003) and
7856		* is from Simon et al. (1994).
7857		*</ol>
7858		*<p>References:
7859		*
7860		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7861		* IERS Technical Note No. 32, BKG (2004)
7862		*
7863		* <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
7864		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
7865		*
7866		*@version 2009 December 16
7867		*
7868		* @since Release 20101201
7869		*
7870		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7871		*/
7872		public static double jauFad03(double t)
7873		{
7874		double a;
7875
7876
7877		/* Mean elongation of the Moon from the Sun (IERS Conventions 2003). */
7878	86	a = fmod( 1072260.703692 +
7879		t * ( 1602961601.2090 +
7880		t * ( - 6.3706 +
7881		t * ( 0.006593 +
7882		t * ( - 0.00003169 ) ) ) ), TURNAS ) * DAS2R;
7883
7884	86	return a;
7885
7886		}
7887
7888
7889		/**
7890		* Fundamental argument, IERS Conventions (2003):
7891		* mean longitude of Earth.
7892		*
7893		*<p>This function is derived from the International Astronomical Union's
7894		* SOFA (Standards Of Fundamental Astronomy) software collection.
7895		*
7896		*<p>Status: canonical model.
7897		*
7898		*<!-- Given: -->
7899		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
7900		*
7901		* <!-- Returned (function value): -->
7902		* @return double mean longitude of Earth, radians (Note 2)
7903		*
7904		* <p>Notes:
7905		* <ol>
7906		*
7907		* <li> Though t is strictly TDB, it is usually more convenient to use
7908		* TT, which makes no significant difference.
7909		*
7910		* <li> The expression used is as adopted in IERS Conventions (2003) and
7911		* comes from Souchay et al. (1999) after Simon et al. (1994).
7912		*</ol>
7913		*<p>References:
7914		*
7915		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7916		* IERS Technical Note No. 32, BKG (2004)
7917		*
7918		* <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
7919		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
7920		*
7921		* <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
7922		* Astron.Astrophys.Supp.Ser. 135, 111
7923		*
7924		*@version 2009 December 16
7925		*
7926		* @since Release 20101201
7927		*
7928		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7929		*/
7930		public static double jauFae03(double t)
7931		{
7932		double a;
7933
7934
7935		/* Mean longitude of Earth (IERS Conventions 2003). */
7936	154	a = fmod(1.753470314 + 628.3075849991 * t, D2PI);
7937
7938	154	return a;
7939
7940		}
7941
7942
7943		/**
7944		* Fundamental argument, IERS Conventions (2003):
7945		* mean longitude of the Moon minus mean longitude of the ascending
7946		* node.
7947		*
7948		*<p>This function is derived from the International Astronomical Union's
7949		* SOFA (Standards Of Fundamental Astronomy) software collection.
7950		*
7951		*<p>Status: canonical model.
7952		*
7953		*<!-- Given: -->
7954		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
7955		*
7956		* <!-- Returned (function value): -->
7957		* @return double F, radians (Note 2)
7958		*
7959		* <p>Notes:
7960		* <ol>
7961		*
7962		* <li> Though t is strictly TDB, it is usually more convenient to use
7963		* TT, which makes no significant difference.
7964		*
7965		* <li> The expression used is as adopted in IERS Conventions (2003) and
7966		* is from Simon et al. (1994).
7967		*</ol>
7968		*<p>References:
7969		*
7970		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
7971		* IERS Technical Note No. 32, BKG (2004)
7972		*
7973		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
7974		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
7975		*
7976		*@version 2009 December 16
7977		*
7978		* @since Release 20101201
7979		*
7980		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
7981		*/
7982		public static double jauFaf03(double t)
7983		{
7984		double a;
7985
7986
7987		/* Mean longitude of the Moon minus that of the ascending node */
7988		/* (IERS Conventions 2003). */
7989	154	a = fmod( 335779.526232 +
7990		t * ( 1739527262.8478 +
7991		t * ( - 12.7512 +
7992		t * ( - 0.001037 +
7993		t * ( 0.00000417 ) ) ) ), TURNAS ) * DAS2R;
7994
7995	154	return a;
7996
7997
7998		}
7999
8000
8001		/**
8002		* Fundamental argument, IERS Conventions (2003):
8003		* mean longitude of Jupiter.
8004		*
8005		*<p>This function is derived from the International Astronomical Union's
8006		* SOFA (Standards Of Fundamental Astronomy) software collection.
8007		*
8008		*<p>Status: canonical model.
8009		*
8010		*<!-- Given: -->
8011		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8012		*
8013		* <!-- Returned (function value): -->
8014		* @return double mean longitude of Jupiter, radians (Note 2)
8015		*
8016		* <p>Notes:
8017		* <ol>
8018		*
8019		* <li> Though t is strictly TDB, it is usually more convenient to use
8020		* TT, which makes no significant difference.
8021		*
8022		* <li> The expression used is as adopted in IERS Conventions (2003) and
8023		* comes from Souchay et al. (1999) after Simon et al. (1994).
8024		*</ol>
8025		*<p>References:
8026		*
8027		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8028		* IERS Technical Note No. 32, BKG (2004)
8029		*
8030		* <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8031		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8032		*
8033		* <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8034		* Astron.Astrophys.Supp.Ser. 135, 111
8035		*
8036		*@version 2009 December 16
8037		*
8038		* @since Release 20101201
8039		*
8040		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8041		*/
8042		public static double jauFaju03(double t)
8043		{
8044		double a;
8045
8046
8047		/* Mean longitude of Jupiter (IERS Conventions 2003). */
8048	72	a = fmod(0.599546497 + 52.9690962641 * t, D2PI);
8049
8050	72	return a;
8051
8052		}
8053
8054
8055		/**
8056		* Fundamental argument, IERS Conventions (2003):
8057		* mean anomaly of the Moon.
8058		*
8059		*<p>This function is derived from the International Astronomical Union's
8060		* SOFA (Standards Of Fundamental Astronomy) software collection.
8061		*
8062		*<p>Status: canonical model.
8063		*
8064		*<!-- Given: -->
8065		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8066		*
8067		* <!-- Returned (function value): -->
8068		* @return double l, radians (Note 2)
8069		*
8070		* <p>Notes:
8071		* <ol>
8072		*
8073		* <li> Though t is strictly TDB, it is usually more convenient to use
8074		* TT, which makes no significant difference.
8075		*
8076		* <li> The expression used is as adopted in IERS Conventions (2003) and
8077		* is from Simon et al. (1994).
8078		*</ol>
8079		*<p>References:
8080		*
8081		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8082		* IERS Technical Note No. 32, BKG (2004)
8083		*
8084		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8085		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8086		*
8087		*@version 2009 December 16
8088		*
8089		* @since Release 20101201
8090		*
8091		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8092		*/
8093		public static double jauFal03(double t)
8094		{
8095		double a;
8096
8097
8098		/* Mean anomaly of the Moon (IERS Conventions 2003). */
8099	154	a = fmod( 485868.249036 +
8100		t * ( 1717915923.2178 +
8101		t * ( 31.8792 +
8102		t * ( 0.051635 +
8103		t * ( - 0.00024470 ) ) ) ), TURNAS ) * DAS2R;
8104
8105	154	return a;
8106
8107		}
8108
8109
8110		/**
8111		* Fundamental argument, IERS Conventions (2003):
8112		* mean anomaly of the Sun.
8113		*
8114		*<p>This function is derived from the International Astronomical Union's
8115		* SOFA (Standards Of Fundamental Astronomy) software collection.
8116		*
8117		*<p>Status: canonical model.
8118		*
8119		*<!-- Given: -->
8120		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8121		*
8122		* <!-- Returned (function value): -->
8123		* @return double l', radians (Note 2)
8124		*
8125		* <p>Notes:
8126		* <ol>
8127		*
8128		* <li> Though t is strictly TDB, it is usually more convenient to use
8129		* TT, which makes no significant difference.
8130		*
8131		* <li> The expression used is as adopted in IERS Conventions (2003) and
8132		* is from Simon et al. (1994).
8133		*</ol>
8134		*<p>References:
8135		*
8136		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8137		* IERS Technical Note No. 32, BKG (2004)
8138		*
8139		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8140		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8141		*
8142		*@version 2009 December 16
8143		*
8144		* @since Release 20101201
8145		*
8146		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8147		*/
8148		public static double jauFalp03(double t)
8149		{
8150		double a;
8151
8152
8153		/* Mean anomaly of the Sun (IERS Conventions 2003). */
8154	86	a = fmod( 1287104.793048 +
8155		t * ( 129596581.0481 +
8156		t * ( - 0.5532 +
8157		t * ( 0.000136 +
8158		t * ( - 0.00001149 ) ) ) ), TURNAS ) * DAS2R;
8159
8160	86	return a;
8161
8162		}
8163
8164
8165		/**
8166		* Fundamental argument, IERS Conventions (2003):
8167		* mean longitude of Mars.
8168		*
8169		*<p>This function is derived from the International Astronomical Union's
8170		* SOFA (Standards Of Fundamental Astronomy) software collection.
8171		*
8172		*<p>Status: canonical model.
8173		*
8174		*<!-- Given: -->
8175		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8176		*
8177		* <!-- Returned (function value): -->
8178		* @return double mean longitude of Mars, radians (Note 2)
8179		*
8180		* <p>Notes:
8181		* <ol>
8182		*
8183		* <li> Though t is strictly TDB, it is usually more convenient to use
8184		* TT, which makes no significant difference.
8185		*
8186		* <li> The expression used is as adopted in IERS Conventions (2003) and
8187		* comes from Souchay et al. (1999) after Simon et al. (1994).
8188		*</ol>
8189		*<p>References:
8190		*
8191		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8192		* IERS Technical Note No. 32, BKG (2004)
8193		*
8194		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8195		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8196		*
8197		* Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8198		* Astron.Astrophys.Supp.Ser. 135, 111
8199		*
8200		*@version 2009 December 16
8201		*
8202		* @since Release 20101201
8203		*
8204		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8205		*/
8206		public static double jauFama03(double t)
8207		{
8208		double a;
8209
8210
8211		/* Mean longitude of Mars (IERS Conventions 2003). */
8212	72	a = fmod(6.203480913 + 334.0612426700 * t, D2PI);
8213
8214	72	return a;
8215
8216		}
8217
8218
8219		/**
8220		* Fundamental argument, IERS Conventions (2003):
8221		* mean longitude of Mercury.
8222		*
8223		*<p>This function is derived from the International Astronomical Union's
8224		* SOFA (Standards Of Fundamental Astronomy) software collection.
8225		*
8226		*<p>Status: canonical model.
8227		*
8228		*<!-- Given: -->
8229		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8230		*
8231		* <!-- Returned (function value): -->
8232		* @return double mean longitude of Mercury, radians (Note 2)
8233		*
8234		* <p>Notes:
8235		* <ol>
8236		*
8237		* <li> Though t is strictly TDB, it is usually more convenient to use
8238		* TT, which makes no significant difference.
8239		*
8240		* <li> The expression used is as adopted in IERS Conventions (2003) and
8241		* comes from Souchay et al. (1999) after Simon et al. (1994).
8242		*</ol>
8243		*<p>References:
8244		*
8245		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8246		* IERS Technical Note No. 32, BKG (2004)
8247		*
8248		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8249		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8250		*
8251		* Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8252		* Astron.Astrophys.Supp.Ser. 135, 111
8253		*
8254		*@version 2009 December 16
8255		*
8256		* @since Release 20101201
8257		*
8258		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8259		*/
8260		public static double jauFame03(double t)
8261		{
8262		double a;
8263
8264
8265		/* Mean longitude of Mercury (IERS Conventions 2003). */
8266	72	a = fmod(4.402608842 + 2608.7903141574 * t, D2PI);
8267
8268	72	return a;
8269
8270		}
8271
8272
8273
8274		/**
8275		* Fundamental argument, IERS Conventions (2003):
8276		* mean longitude of Neptune.
8277		*
8278		*<p>This function is derived from the International Astronomical Union's
8279		* SOFA (Standards Of Fundamental Astronomy) software collection.
8280		*
8281		*<p>Status: canonical model.
8282		*
8283		*<!-- Given: -->
8284		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8285		*
8286		* <!-- Returned (function value): -->
8287		* @return double mean longitude of Neptune, radians (Note 2)
8288		*
8289		* <p>Notes:
8290		* <ol>
8291		*
8292		* <li> Though t is strictly TDB, it is usually more convenient to use
8293		* TT, which makes no significant difference.
8294		*
8295		* <li> The expression used is as adopted in IERS Conventions (2003) and
8296		* is adapted from Simon et al. (1994).
8297		*</ol>
8298		*<p>References:
8299		*
8300		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8301		* IERS Technical Note No. 32, BKG (2004)
8302		*
8303		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8304		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8305		*
8306		*@version 2009 December 16
8307		*
8308		* @since Release 20101201
8309		*
8310		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8311		*/
8312		public static double jauFane03(double t)
8313		{
8314		double a;
8315
8316
8317		/* Mean longitude of Neptune (IERS Conventions 2003). */
8318	4	a = fmod(5.311886287 + 3.8133035638 * t, D2PI);
8319
8320	4	return a;
8321
8322		}
8323
8324
8325		/**
8326		* Fundamental argument, IERS Conventions (2003):
8327		* mean longitude of the Moon's ascending node.
8328		*
8329		*<p>This function is derived from the International Astronomical Union's
8330		* SOFA (Standards Of Fundamental Astronomy) software collection.
8331		*
8332		*<p>Status: canonical model.
8333		*
8334		*<!-- Given: -->
8335		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8336		*
8337		* <!-- Returned (function value): -->
8338		* @return double Omega, radians (Note 2)
8339		*
8340		* <p>Notes:
8341		* <ol>
8342		*
8343		* <li> Though t is strictly TDB, it is usually more convenient to use
8344		* TT, which makes no significant difference.
8345		*
8346		* <li> The expression used is as adopted in IERS Conventions (2003) and
8347		* is from Simon et al. (1994).
8348		*</ol>
8349		*<p>References:
8350		*
8351		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8352		* IERS Technical Note No. 32, BKG (2004)
8353		*
8354		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8355		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8356		*
8357		*@version 2009 December 16
8358		*
8359		* @since Release 20101201
8360		*
8361		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8362		*/
8363		public static double jauFaom03(double t)
8364		{
8365		double a;
8366
8367
8368		/* Mean longitude of the Moon's ascending node */
8369		/* (IERS Conventions 2003). */
8370	154	a = fmod( 450160.398036 +
8371		t * ( - 6962890.5431 +
8372		t * ( 7.4722 +
8373		t * ( 0.007702 +
8374		t * ( - 0.00005939 ) ) ) ), TURNAS ) * DAS2R;
8375
8376	154	return a;
8377
8378		}
8379
8380
8381		/**
8382		* Fundamental argument, IERS Conventions (2003):
8383		* general accumulated precession in longitude.
8384		*
8385		*<p>This function is derived from the International Astronomical Union's
8386		* SOFA (Standards Of Fundamental Astronomy) software collection.
8387		*
8388		*<p>Status: canonical model.
8389		*
8390		*<!-- Given: -->
8391		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8392		*
8393		* <!-- Returned (function value): -->
8394		* @return double general precession in longitude, radians (Note 2)
8395		*
8396		* <p>Notes:
8397		* <ol>
8398		*
8399		* <li> Though t is strictly TDB, it is usually more convenient to use
8400		* TT, which makes no significant difference.
8401		*
8402		* <li> The expression used is as adopted in IERS Conventions (2003). It
8403		* is taken from Kinoshita & Souchay (1990) and comes originally
8404		* from Lieske et al. (1977).
8405		*</ol>
8406		*<p>References:
8407		*
8408		* Kinoshita, H. and Souchay J. 1990, Celest.Mech. and Dyn.Astron.
8409		* 48, 187
8410		*
8411		* <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
8412		* Astron.Astrophys. 58, 1-16
8413		*
8414		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8415		* IERS Technical Note No. 32, BKG (2004)
8416		*
8417		*@version 2009 December 16
8418		*
8419		* @since Release 20101201
8420		*
8421		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8422		*/
8423		public static double jauFapa03(double t)
8424		{
8425		double a;
8426
8427
8428		/* General accumulated precession in longitude. */
8429	154	a = (0.024381750 + 0.00000538691 * t) * t;
8430
8431	154	return a;
8432
8433		}
8434
8435
8436		/**
8437		* Fundamental argument, IERS Conventions (2003):
8438		* mean longitude of Saturn.
8439		*
8440		*<p>This function is derived from the International Astronomical Union's
8441		* SOFA (Standards Of Fundamental Astronomy) software collection.
8442		*
8443		*<p>Status: canonical model.
8444		*
8445		*<!-- Given: -->
8446		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8447		*
8448		* <!-- Returned (function value): -->
8449		* @return double mean longitude of Saturn, radians (Note 2)
8450		*
8451		* <p>Notes:
8452		* <ol>
8453		*
8454		* <li> Though t is strictly TDB, it is usually more convenient to use
8455		* TT, which makes no significant difference.
8456		*
8457		* <li> The expression used is as adopted in IERS Conventions (2003) and
8458		* comes from Souchay et al. (1999) after Simon et al. (1994).
8459		*</ol>
8460		*<p>References:
8461		*
8462		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8463		* IERS Technical Note No. 32, BKG (2004)
8464		*
8465		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8466		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8467		*
8468		* Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8469		* Astron.Astrophys.Supp.Ser. 135, 111
8470		*
8471		*@version 2009 December 16
8472		*
8473		* @since Release 20101201
8474		*
8475		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8476		*/
8477		public static double jauFasa03(double t)
8478		{
8479		double a;
8480
8481
8482		/* Mean longitude of Saturn (IERS Conventions 2003). */
8483	72	a = fmod(0.874016757 + 21.3299104960 * t, D2PI);
8484
8485	72	return a;
8486
8487		}
8488
8489
8490		/**
8491		* Fundamental argument, IERS Conventions (2003):
8492		* mean longitude of Uranus.
8493		*
8494		*<p>This function is derived from the International Astronomical Union's
8495		* SOFA (Standards Of Fundamental Astronomy) software collection.
8496		*
8497		*<p>Status: canonical model.
8498		*
8499		*<!-- Given: -->
8500		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8501		*
8502		* Returned (function value):
8503		* double mean longitude of Uranus, radians (Note 2)
8504		*
8505		* <p>Notes:
8506		* <ol>
8507		*
8508		* <li> Though t is strictly TDB, it is usually more convenient to use
8509		* TT, which makes no significant difference.
8510		*
8511		* <li> The expression used is as adopted in IERS Conventions (2003) and
8512		* is adapted from Simon et al. (1994).
8513		*</ol>
8514		*<p>References:
8515		*
8516		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8517		* IERS Technical Note No. 32, BKG (2004)
8518		*
8519		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8520		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8521		*
8522		*@version 2009 December 16
8523		*
8524		* @since Release 20101201
8525		*
8526		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8527		*/
8528		public static double jauFaur03(double t)
8529		{
8530		double a;
8531
8532
8533		/* Mean longitude of Uranus (IERS Conventions 2003). */
8534	72	a = fmod(5.481293872 + 7.4781598567 * t, D2PI);
8535
8536	72	return a;
8537
8538		}
8539
8540
8541		/**
8542		* Fundamental argument, IERS Conventions (2003):
8543		* mean longitude of Venus.
8544		*
8545		*<p>This function is derived from the International Astronomical Union's
8546		* SOFA (Standards Of Fundamental Astronomy) software collection.
8547		*
8548		*<p>Status: canonical model.
8549		*
8550		*<!-- Given: -->
8551		* @param t double TDB, Julian centuries since J2000.0 (Note 1)
8552		*
8553		* <!-- Returned (function value): -->
8554		* @return double mean longitude of Venus, radians (Note 2)
8555		*
8556		* <p>Notes:
8557		* <ol>
8558		*
8559		* <li> Though t is strictly TDB, it is usually more convenient to use
8560		* TT, which makes no significant difference.
8561		*
8562		* <li> The expression used is as adopted in IERS Conventions (2003) and
8563		* comes from Souchay et al. (1999) after Simon et al. (1994).
8564		*</ol>
8565		*<p>References:
8566		*
8567		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
8568		* IERS Technical Note No. 32, BKG (2004)
8569		*
8570		* Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
8571		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
8572		*
8573		* Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
8574		* Astron.Astrophys.Supp.Ser. 135, 111
8575		*
8576		*@version 2009 December 16
8577		*
8578		* @since Release 20101201
8579		*
8580		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8581		*/
8582		public static double jauFave03(double t)
8583		{
8584		double a;
8585
8586
8587		/* Mean longitude of Venus (IERS Conventions 2003). */
8588	154	a = fmod(3.176146697 + 1021.3285546211 * t, D2PI);
8589
8590	154	return a;
8591
8592		}
8593
8594
8595		/**
8596		* Transform FK5 (J2000.0) star data into the Hipparcos system.
8597		*
8598		*<p>This function is derived from the International Astronomical Union's
8599		* SOFA (Standards Of Fundamental Astronomy) software collection.
8600		*
8601		*<p>Status: support function.
8602		*
8603		* Given (all FK5, equinox J2000.0, epoch J2000.0):
8604		* r5 double RA (radians)
8605		* d5 double Dec (radians)
8606		* dr5 double proper motion in RA (dRA/dt, rad/Jyear)
8607		* dd5 double proper motion in Dec (dDec/dt, rad/Jyear)
8608		* px5 double parallax (arcsec)
8609		* rv5 double radial velocity (km/s, positive = receding)
8610		*
8611		* Returned (all Hipparcos, epoch J2000.0):
8612		* rh double RA (radians)
8613		* dh double Dec (radians)
8614		* drh double proper motion in RA (dRA/dt, rad/Jyear)
8615		* ddh double proper motion in Dec (dDec/dt, rad/Jyear)
8616		* pxh double parallax (arcsec)
8617		* rvh double radial velocity (km/s, positive = receding)
8618		*
8619		* <p>Notes:
8620		* <ol>
8621		*
8622		* <li> This function transforms FK5 star positions and proper motions
8623		* into the system of the Hipparcos catalog.
8624		*
8625		* <li> The proper motions in RA are dRA/dt rather than
8626		* cos(Dec)*dRA/dt, and are per year rather than per century.
8627		*
8628		* <li> The FK5 to Hipparcos transformation is modeled as a pure
8629		* rotation and spin; zonal errors in the FK5 catalog are not
8630		* taken into account.
8631		*
8632		* <li> See also {@link #jauH2fk5}, {@link #jauFk5hz}, {@link #jauHfk5z}.
8633		*</ol>
8634		*<p>Called:<ul>
8635		* <li>{@link #jauStarpv} star catalog data to space motion pv-vector
8636		* <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
8637		* <li>{@link #jauRxp} product of r-matrix and p-vector
8638		* <li>{@link #jauPxp} vector product of two p-vectors
8639		* <li>{@link #jauPpp} p-vector plus p-vector
8640		* <li>{@link #jauPvstar} space motion pv-vector to star catalog data
8641		* </ul>
8642		*<p>Reference:
8643		*
8644		* <p>F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
8645		*
8646		*@version 2009 December 17
8647		*
8648		* @since Release 20101201
8649		*
8650		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8651		*/
8652		public static CatalogCoords jauFk52h(double r5, double d5,
8653		double dr5, double dd5, double px5, double rv5)
8654		{
8655		int i;
8656	2	double pv5[][] = new double[2][3], r5h[][] = new double[3][3], s5h[] = new double[3], wxp[] = new double[3], vv[] = new double[3], pvh[][] = new double[2][3];
8657
8658
8659		/* FK5 barycentric position/velocity pv-vector (normalized). */
8660	2	jauStarpv(r5, d5, dr5, dd5, px5, rv5, pv5);
8661
8662		/* FK5 to Hipparcos orientation matrix and spin vector. */
8663	2	jauFk5hip(r5h, s5h);
8664
8665		/* Make spin units per day instead of per year. */
8666	2	for ( i = 0; i < 3; s5h[i++] /= 365.25 );
8667
8668		/* Orient the FK5 position into the Hipparcos system. */
8669	2	pvh[0] = jauRxp(r5h, pv5[0]);
8670
8671		/* Apply spin to the position giving an extra space motion component. */
8672	2	wxp = jauPxp(pv5[0],s5h);
8673
8674		/* Add this component to the FK5 space motion. */
8675	2	vv = jauPpp(wxp, pv5[1]);
8676
8677		/* Orient the FK5 space motion into the Hipparcos system. */
8678	2	pvh[1] = jauRxp(r5h, vv);
8679
8680		/* Hipparcos pv-vector to spherical. */
8681	2	CatalogCoords cat = null;
8682		try {
8683	2	cat = jauPvstar(pvh);
8684	0	} catch (JSOFAInternalError e) {
8685		//original code ignored possibility of error too...
8686	0	e.printStackTrace();
8687	2	}
8688
8689	2	return cat;
8690
8691		}
8692
8693
8694		/**
8695		* FK5 to Hipparcos rotation and spin.
8696		*
8697		*<p>This function is derived from the International Astronomical Union's
8698		* SOFA (Standards Of Fundamental Astronomy) software collection.
8699		*
8700		*<p>Status: support function.
8701		*
8702		*<!-- Returned: -->
8703		* @param r5h double[3][3] <u>returned</u> r-matrix: FK5 rotation wrt Hipparcos (Note 2)
8704		* @param s5h double[3] <u>returned</u> r-vector: FK5 spin wrt Hipparcos (Note 3)
8705		*
8706		* <p>Notes:
8707		* <ol>
8708		*
8709		* <li> This function models the FK5 to Hipparcos transformation as a
8710		* pure rotation and spin; zonal errors in the FK5 catalogue are
8711		* not taken into account.
8712		*
8713		* <li> The r-matrix r5h operates in the sense:
8714		*
8715		* P_Hipparcos = r5h x P_FK5
8716		*
8717		* where P_FK5 is a p-vector in the FK5 frame, and P_Hipparcos is
8718		* the equivalent Hipparcos p-vector.
8719		*
8720		* <li> The r-vector s5h represents the time derivative of the FK5 to
8721		* Hipparcos rotation. The units are radians per year (Julian,
8722		* TDB).
8723		*</ol>
8724		*<p>Called:<ul>
8725		* <li>{@link #jauRv2m} r-vector to r-matrix
8726		* </ul>
8727		*<p>Reference:
8728		*
8729		* <p>F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
8730		*
8731		*@version 2009 March 14
8732		*
8733		* @since Release 20101201
8734		*
8735		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8736		*/
8737		public static void jauFk5hip(double r5h[][], double s5h[] )
8738		{
8739	10	double v[] = new double[3];
8740
8741		/* FK5 wrt Hipparcos orientation and spin (radians, radians/year) */
8742		double epx, epy, epz;
8743		double omx, omy, omz;
8744
8745
8746	10	epx = -19.9e-3 * DAS2R;
8747	10	epy = -9.1e-3 * DAS2R;
8748	10	epz = 22.9e-3 * DAS2R;
8749
8750	10	omx = -0.30e-3 * DAS2R;
8751	10	omy = 0.60e-3 * DAS2R;
8752	10	omz = 0.70e-3 * DAS2R;
8753
8754		/* FK5 to Hipparcos orientation expressed as an r-vector. */
8755	10	v[0] = epx;
8756	10	v[1] = epy;
8757	10	v[2] = epz;
8758
8759		/* Re-express as an r-matrix. */
8760	10	double[][] r5ht = jauRv2m(v);
8761	10	jauCr(r5ht, r5h);
8762
8763		/* Hipparcos wrt FK5 spin expressed as an r-vector. */
8764	10	s5h[0] = omx;
8765	10	s5h[1] = omy;
8766	10	s5h[2] = omz;
8767
8768	10	return;
8769
8770		}
8771
8772		/**
8773		* Position consisting of (α, δ) pairs in radians. Where α is right ascension (or longitude angle) and δ is declination (or latitude angle).
8774		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
8775		*
8776		* @since AIDA Stage 1
8777		* @TODO needs better name cf {@link SphericalPosition}
8778		*/
8779		public static class SphericalCoordinate {
8780		public double alpha;
8781		public double delta;
8782	88	public SphericalCoordinate(double alpha, double delta){
8783	88	this.alpha = alpha;
8784	88	this.delta = delta;
8785	88	}
8786		}
8787
8788		/**
8789		* Spherical coordinate with equation of origins .
8790		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Mar 2014
8791		* @version $Revision$ $date$
8792		*/
8793		public static class SphericalCoordinateEO {
8794		SphericalCoordinate pos;
8795		double eo;
8796		/**
8797		* @param pos
8798		* @param eo
8799		*/
8800	4	public SphericalCoordinateEO(SphericalCoordinate pos, double eo) {
8801	4	this.pos = pos;
8802	4	this.eo = eo;
8803	4	}
8804
8805
8806		}
8807		/**
8808		* Transform an FK5 (J2000.0) star position into the system of the
8809		* Hipparcos catalogue, assuming zero Hipparcos proper motion.
8810		*
8811		*<p>This function is derived from the International Astronomical Union's
8812		* SOFA (Standards Of Fundamental Astronomy) software collection.
8813		*
8814		*<p>Status: support function.
8815		*
8816		*<!-- Given: -->
8817		* @param r5 double FK5 RA (radians), equinox J2000.0, at date
8818		* @param d5 double FK5 Dec (radians), equinox J2000.0, at date
8819		* @param date1 double TDB date (Notes 1,2)
8820		* @param date2 double TDB date (Notes 1,2)
8821		*
8822		*<!-- Returned: -->
8823		* @return rh double <u>returned</u> Hipparcos RA (radians)
8824		* dh double <u>returned</u> Hipparcos Dec (radians)
8825		*
8826		* <p>Notes:
8827		* <ol>
8828		*
8829		* <li> This function converts a star position from the FK5 system to
8830		* the Hipparcos system, in such a way that the Hipparcos proper
8831		* motion is zero. Because such a star has, in general, a non-zero
8832		* proper motion in the FK5 system, the function requires the date
8833		* at which the position in the FK5 system was determined.
8834		*
8835		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
8836		* convenient way between the two arguments. For example,
8837		* JD(TT)=2450123.7 could be expressed in any of these ways,
8838		* among others:
8839		*<pre>
8840		* date1 date2
8841		*
8842		* 2450123.7 0.0 (JD method)
8843		* 2451545.0 -1421.3 (J2000 method)
8844		* 2400000.5 50123.2 (MJD method)
8845		* 2450123.5 0.2 (date & time method)
8846		*</pre>
8847		* The JD method is the most natural and convenient to use in
8848		* cases where the loss of several decimal digits of resolution
8849		* is acceptable. The J2000 method is best matched to the way
8850		* the argument is handled internally and will deliver the
8851		* optimum resolution. The MJD method and the date & time methods
8852		* are both good compromises between resolution and convenience.
8853		*
8854		* <li> The FK5 to Hipparcos transformation is modeled as a pure
8855		* rotation and spin; zonal errors in the FK5 catalogue are not
8856		* taken into account.
8857		*
8858		* <li> The position returned by this function is in the Hipparcos
8859		* reference system but at date date1+date2.
8860		*
8861		* <li> See also jauFk52h, jauH2fk5, jauHfk5z.
8862		*</ol>
8863		*<p>Called:<ul>
8864		* <li>{@link #jauS2c} spherical coordinates to unit vector
8865		* <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
8866		* <li>{@link #jauSxp} multiply p-vector by scalar
8867		* <li>{@link #jauRv2m} r-vector to r-matrix
8868		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
8869		* <li>{@link #jauPxp} vector product of two p-vectors
8870		* <li>{@link #jauC2s} p-vector to spherical
8871		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
8872		* </ul>
8873		*<p>Reference:
8874		*
8875		* <p>F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
8876		*
8877		*@version 2009 December 17
8878		*
8879		* @since Release 20101201
8880		*
8881		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8882		*/
8883		public static SphericalCoordinate jauFk5hz(double r5, double d5, double date1, double date2
8884		)
8885		{
8886	2	double t, p5e[] = new double[3], r5h[][] = new double[3][3], s5h[] = new double[3], vst[] = new double[3], rst[][] = new double[3][3], p5[] = new double[3],
8887	2	ph[] = new double[3];
8888
8889
8890		/* Interval from given date to fundamental epoch J2000.0 (JY). */
8891	2	t = - ((date1 - DJ00) + date2) / DJY;
8892
8893		/* FK5 barycentric position vector. */
8894	2	p5e = jauS2c(r5,d5);
8895
8896		/* FK5 to Hipparcos orientation matrix and spin vector. */
8897	2	jauFk5hip(r5h, s5h);
8898
8899		/* Accumulated Hipparcos wrt FK5 spin over that interval. */
8900	2	vst = jauSxp(t,s5h);
8901
8902		/* Express the accumulated spin as a rotation matrix. */
8903	2	rst = jauRv2m(vst);
8904
8905		/* Derotate the vector's FK5 axes back to date. */
8906	2	p5 = jauTrxp(rst, p5e);
8907
8908		/* Rotate the vector into the Hipparcos system. */
8909	2	ph = jauRxp(r5h, p5);
8910
8911		/* Hipparcos vector to spherical. */
8912	2	SphericalCoordinate sc = jauC2s(ph);
8913	2	double rh = jauAnp(sc.alpha);
8914	2	sc.alpha = rh;
8915
8916	2	return sc;
8917
8918		}
8919
8920
8921		/**
8922		* Form rotation matrix given the Fukushima-Williams angles.
8923		*
8924		*<p>This function is derived from the International Astronomical Union's
8925		* SOFA (Standards Of Fundamental Astronomy) software collection.
8926		*
8927		*<p>Status: support function.
8928		*
8929		*<!-- Given: -->
8930		* @param gamb double F-W angle gamma_bar (radians)
8931		* @param phib double F-W angle phi_bar (radians)
8932		* @param psi double F-W angle psi (radians)
8933		* @param eps double F-W angle epsilon (radians)
8934		*
8935		*<!-- Returned: -->
8936		* @return r double[3][3] <u>returned</u> rotation matrix
8937		*
8938		* <p>Notes:
8939		* <ol>
8940		*
8941		* <li> Naming the following points:
8942		*
8943		* e = J2000.0 ecliptic pole,
8944		* p = GCRS pole,
8945		* E = ecliptic pole of date,
8946		* and P = CIP,
8947		*
8948		* the four Fukushima-Williams angles are as follows:
8949		*
8950		* gamb = gamma = epE
8951		* phib = phi = pE
8952		* psi = psi = pEP
8953		* eps = epsilon = EP
8954		*
8955		* <li> The matrix representing the combined effects of frame bias,
8956		* precession and nutation is:
8957		*
8958		* NxPxB = R_1(-eps).R_3(-psi).R_1(phib).R_3(gamb)
8959		*
8960		* <li> Three different matrices can be constructed, depending on the
8961		* supplied angles:
8962		*
8963		* o To obtain the nutation x precession x frame bias matrix,
8964		* generate the four precession angles, generate the nutation
8965		* components and add them to the psi_bar and epsilon_A angles,
8966		* and call the present function.
8967		*
8968		* o To obtain the precession x frame bias matrix, generate the
8969		* four precession angles and call the present function.
8970		*
8971		* o To obtain the frame bias matrix, generate the four precession
8972		* angles for date J2000.0 and call the present function.
8973		*
8974		* The nutation-only and precession-only matrices can if necessary
8975		* be obtained by combining these three appropriately.
8976		*</ol>
8977		*<p>Called:<ul>
8978		* <li>{@link #jauIr} initialize r-matrix to identity
8979		* <li>{@link #jauRz} rotate around Z-axis
8980		* <li>{@link #jauRx} rotate around X-axis
8981		* </ul>
8982		*<p>Reference:
8983		*
8984		* Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
8985		*
8986		*@version 2009 December 17
8987		*
8988		* @since Release 20101201
8989		*
8990		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
8991		*/
8992		public static double[][] jauFw2m(double gamb, double phib, double psi, double eps)
8993		{
8994		/* Construct the matrix. */
8995	72	double r[][] = new double[3][3];
8996	72	jauIr(r);
8997	72	jauRz(gamb, r);
8998	72	jauRx(phib, r);
8999	72	jauRz(-psi, r);
9000	72	jauRx(-eps, r);
9001
9002	72	return r;
9003
9004		}
9005
9006
9007		/**
9008		* CIP X,Y given Fukushima-Williams bias-precession-nutation angles.
9009		*
9010		*<p>This function is derived from the International Astronomical Union's
9011		* SOFA (Standards Of Fundamental Astronomy) software collection.
9012		*
9013		*<p>Status: support function.
9014		*
9015		*<!-- Given: -->
9016		* @param gamb double F-W angle gamma_bar (radians)
9017		* @param phib double F-W angle phi_bar (radians)
9018		* @param psi double F-W angle psi (radians)
9019		* @param eps double F-W angle epsilon (radians)
9020		*
9021		*<!-- Returned: -->
9022		* @return CIP unit vector X,Y
9023		*
9024		* <p>Notes:
9025		* <ol>
9026		*
9027		* <li> Naming the following points:
9028		*
9029		* e = J2000.0 ecliptic pole,
9030		* p = GCRS pole
9031		* E = ecliptic pole of date,
9032		* and P = CIP,
9033		*
9034		* the four Fukushima-Williams angles are as follows:
9035		*
9036		* gamb = gamma = epE
9037		* phib = phi = pE
9038		* psi = psi = pEP
9039		* eps = epsilon = EP
9040		*
9041		* <li> The matrix representing the combined effects of frame bias,
9042		* precession and nutation is:
9043		*
9044		* NxPxB = R_1(-epsA).R_3(-psi).R_1(phib).R_3(gamb)
9045		*
9046		* The returned values x,y are elements [2][0] and [2][1] of the
9047		* matrix. Near J2000.0, they are essentially angles in radians
9048		*
9049		* X,Y are elements (3,1) and (3,2) of the matrix.
9050		*</ol>
9051		*<p>Called:<ul>
9052		* <li>{@link #jauFw2m} F-W angles to r-matrix
9053		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
9054		* </ul>
9055		*<p>Reference:
9056		*
9057		* Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
9058		*
9059		*@version 2009 December 17
9060		*
9061		* @since Release 20101201
9062		*
9063		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9064		*/
9065		public static CelestialIntermediatePole jauFw2xy(double gamb, double phib, double psi, double eps)
9066		{
9067	2	double r[][] = new double[3][3];
9068
9069
9070		/* Form NxPxB matrix. */
9071	2	r = jauFw2m(gamb, phib, psi, eps);
9072
9073		/* Extract CIP X,Y. */
9074	2	return jauBpn2xy(r);
9075
9076		}
9077
9078		/**
9079		* Geodetic coordinates.
9080		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
9081		*
9082		* @since AIDA Stage 1
9083		*/
9084		public static class GeodeticCoord {
9085		/** longitude (radians, east +ve) */
9086		public double elong;
9087		/** latitude (geodetic, radians) */
9088		public double phi;
9089		/** height above ellipsoid (geodetic) */
9090		public double height;
9091	8	public GeodeticCoord(double elong, double phi, double height) {
9092	8	this.elong = elong;
9093	8	this.phi = phi;
9094	8	this.height = height;
9095	8	}
9096		}
9097		/**
9098		* Transform geocentric coordinates to geodetic using the specified
9099		* reference ellipsoid.
9100		*
9101		*<p>This function is derived from the International Astronomical Union's
9102		* JSOFA (Standards of Fundamental Astronomy) software collection.
9103		*
9104		*<p>Status: canonical transformation.
9105		*
9106		*<!-- Given: -->
9107		* @param n int ellipsoid identifier (Note 1)
9108		* @param xyz double[3] geocentric vector (Note 2)
9109		*
9110		*<!-- Returned: -->
9111		* @return elong double <u>returned</u> longitude (radians, east +ve)
9112		* phi double <u>returned</u> latitude (geodetic, radians, Note 3)
9113		* height double <u>returned</u> height above ellipsoid (geodetic, Notes 2,3)
9114		*
9115		* <!-- Returned (function value): -->
9116		* @throws JSOFAIllegalParameter
9117		* 0 = OK
9118		* -1 = illegal identifier (Note 3)
9119		* -2 = internal error (Note 3)
9120		*
9121		* <p>Notes:
9122		* <ol>
9123		*
9124		* <li> The identifier n is a number that specifies the choice of
9125		* reference ellipsoid. The following are supported:
9126		*
9127		* n ellipsoid
9128		*
9129		* 1 WGS84
9130		* 2 GRS80
9131		*
9132		* The number n has no significance outside the JSOFA software.
9133		*
9134		* <li> The geocentric vector (xyz, given) and height (height, returned)
9135		* are in meters.
9136		*
9137		* <li> An error status -1 means that the identifier n is illegal. An
9138		* error status -2 is theoretically impossible. In all error cases,
9139		* phi and height are both set to -1e9.
9140		*
9141		* <li> The inverse transformation is performed in the function jauGd2gc.
9142		*</ol>
9143		*<p>Called:<ul>
9144		* <li>{@link #jauEform} Earth reference ellipsoids
9145		* <li>{@link #jauGc2gde} geocentric to geodetic transformation, general
9146		* </ul>
9147		*@version 2010 January 18
9148		*
9149		* @since Release 20101201
9150		*
9151		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9152		*/
9153		public static GeodeticCoord jauGc2gd ( int n, double xyz[] ) throws JSOFAIllegalParameter
9154		{
9155		GeodeticCoord gc;
9156
9157
9158		/* Obtain reference ellipsoid parameters. */
9159	10	ReferenceEllipsoid el = jauEform ( n );
9160
9161		/* If OK, transform x,y,z to longitude, geodetic latitude, height. */
9162	6	gc = jauGc2gde ( el.a, el.f, xyz);
9163
9164		/* Return the status. */
9165	6	return gc;
9166
9167
9168		}
9169
9170		/**
9171		* Transform geocentric coordinates to geodetic for a reference
9172		* ellipsoid of specified form.
9173		*
9174		*<p>This function is derived from the International Astronomical Union's
9175		* JSOFA (Standards of Fundamental Astronomy) software collection.
9176		*
9177		*<p>Status: support function.
9178		*
9179		*<!-- Given: -->
9180		* @param a double equatorial radius (Notes 2,4)
9181		* @param f double flattening (Note 3)
9182		* @param xyz double[3] geocentric vector (Note 4)
9183		*
9184		*<!-- Returned: -->
9185		* @return GeodeticCoord logitude (radians, east +ve) latitude (geodetic, radians) height above ellipsoid (geodetic, Note 4)
9186		*
9187		* @throws JSOFAIllegalParameter
9188		* int status:
9189		*
9190		* -1 = illegal a
9191		* -2 = illegal f
9192		*
9193		* <p>Notes:
9194		* <ol>
9195		*
9196		* <li> This function is based on the GCONV2H Fortran subroutine by
9197		* Toshio Fukushima (see reference).
9198		*
9199		* <li> The equatorial radius, a, can be in any units, but meters is
9200		* the conventional choice.
9201		*
9202		* <li> The flattening, f, is (for the Earth) a value around 0.00335,
9203		* i.e. around 1/298.
9204		*
9205		* <li> The equatorial radius, a, and the geocentric vector, xyz,
9206		* must be given in the same units, and determine the units of
9207		* the returned height, height.
9208		*
9209		* <li> If an error occurs (status < 0), elong, phi and height are
9210		* unchanged.
9211		*
9212		* <li> The inverse transformation is performed in the function
9213		* jauGd2gce.
9214		*
9215		* <li> The transformation for a standard ellipsoid (such as WGS84) can
9216		* more conveniently be performed by calling jauGc2gd, which uses a
9217		* numerical code (1 for WGS84) to identify the required A and F
9218		* values.
9219		*</ol>
9220		*<p>Reference:
9221		*
9222		* Fukushima, T., "Transformation from Cartesian to geodetic
9223		* coordinates accelerated by Halley's method", J.Geodesy (2006)
9224		* 79: 689-693
9225		*
9226		*@version 2009 November 2
9227		*
9228		* @since Release 20101201
9229		*
9230		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9231		*
9232		*/
9233		public static GeodeticCoord jauGc2gde ( double a, double f, double xyz[] ) throws JSOFAIllegalParameter
9234		{
9235		double aeps2, e2, e4t, ec2, ec, b, x, y, z, p2, absz, p, s0, pn, zc,
9236		c0, c02, c03, s02, s03, a02, a0, a03, d0, f0, b0, s1,
9237		cc, s12, cc2;
9238
9239		double phi, height;
9240		/* ------------- */
9241		/* Preliminaries */
9242		/* ------------- */
9243
9244		/* Validate ellipsoid parameters. */
9245	8	if ( f < 0.0 \|\| f >= 1.0 ) throw new JSOFAIllegalParameter("bad f", -1);
9246	8	if ( a <= 0.0 ) throw new JSOFAIllegalParameter("bad a", -2);
9247
9248		/* Functions of ellipsoid parameters (with further validation of f). */
9249	8	aeps2 = aa 1e-32;
9250	8	e2 = (2.0 - f) * f;
9251	8	e4t = e2e2 1.5;
9252	8	ec2 = 1.0 - e2;
9253	8	if ( ec2 <= 0.0 ) throw new JSOFAIllegalParameter("bad f", -1);
9254	8	ec = sqrt(ec2);
9255	8	b = a * ec;
9256
9257		/* Cartesian components. */
9258	8	x = xyz[0];
9259	8	y = xyz[1];
9260	8	z = xyz[2];
9261
9262		/* Distance from polar axis squared. */
9263	8	p2 = xx + yy;
9264
9265		/* Longitude. */
9266	8	double elong = p2 > 0.0 ? atan2(y, x) : 0.0;
9267
9268		/* Unsigned z-coordinate. */
9269	8	absz = abs(z);
9270
9271		/* Proceed unless polar case. */
9272	8	if ( p2 > aeps2 ) {
9273
9274		/* Distance from polar axis. */
9275	8	p = sqrt(p2);
9276
9277		/* Normalization. */
9278	8	s0 = absz / a;
9279	8	pn = p / a;
9280	8	zc = ec * s0;
9281
9282		/* Prepare Newton correction factors. */
9283	8	c0 = ec * pn;
9284	8	c02 = c0 * c0;
9285	8	c03 = c02 * c0;
9286	8	s02 = s0 * s0;
9287	8	s03 = s02 * s0;
9288	8	a02 = c02 + s02;
9289	8	a0 = sqrt(a02);
9290	8	a03 = a02 * a0;
9291	8	d0 = zca03 + e2s03;
9292	8	f0 = pna03 - e2c03;
9293
9294		/* Prepare Halley correction factor. */
9295	8	b0 = e4t * s02 * c02 * pn * (a0 - ec);
9296	8	s1 = d0f0 - b0s0;
9297	8	cc = ec * (f0f0 - b0c0);
9298
9299		/* Evaluate latitude and height. */
9300	8	phi = atan(s1/cc);
9301	8	s12 = s1 * s1;
9302	8	cc2 = cc * cc;
9303	8	height = (pcc + abszs1 - a * sqrt(ec2*s12 + cc2)) /
9304	8	sqrt(s12 + cc2);
9305		} else {
9306
9307		/* Exception: pole. */
9308	0	phi = DPI / 2.0;
9309	0	height = absz - b;
9310		}
9311
9312		/* Restore sign of latitude. */
9313	8	if ( z < 0 ) phi = -phi;
9314
9315		/* OK status. */
9316	8	return new GeodeticCoord(elong, phi, height);
9317
9318
9319		}
9320
9321
9322		/**
9323		* Transform geodetic coordinates to geocentric using the specified
9324		* reference ellipsoid.
9325		*
9326		*<p>This function is derived from the International Astronomical Union's
9327		* JSOFA (Standards of Fundamental Astronomy) software collection.
9328		*
9329		*<p>Status: canonical transformation.
9330		*
9331		*<!-- Given: -->
9332		* @param n int ellipsoid identifier (Note 1)
9333		* @param elong double longitude (radians, east +ve)
9334		* @param phi double latitude (geodetic, radians, Note 3)
9335		* @param height double height above ellipsoid (geodetic, Notes 2,3)
9336		*
9337		*<!-- Returned: -->
9338		* @return xyz double[3] <u>returned</u> geocentric vector (Note 2)
9339		*
9340		* <!-- Returned (function value): -->
9341		* @throws JSOFAIllegalParameter
9342		* -1 = illegal identifier (Note 3)
9343		* -2 = illegal case (Note 3)
9344		*
9345		* <p>Notes:
9346		* <ol>
9347		*
9348		* <li> The identifier n is a number that specifies the choice of
9349		* reference ellipsoid. The following are supported:
9350		*
9351		* n ellipsoid
9352		*
9353		* 1 WGS84
9354		* 2 GRS80
9355		*
9356		* The number n has no significance outside the JSOFA software.
9357		*
9358		* <li> The height (height, given) and the geocentric vector (xyz,
9359		* returned) are in meters.
9360		*
9361		* <li> No validation is performed on the arguments elong, phi and
9362		* height. An error status -1 means that the identifier n is
9363		* illegal. An error status -2 protects against cases that would
9364		* lead to arithmetic exceptions. In all error cases, xyz is set
9365		* to zeros.
9366		*
9367		* <li> The inverse transformation is performed in the function jauGc2gd.
9368		*</ol>
9369		*<p>Called:<ul>
9370		* <li>{@link #jauEform} Earth reference ellipsoids
9371		* <li>{@link #jauGd2gce} geodetic to geocentric transformation, general
9372		* <li>{@link #jauZp} zero p-vector
9373		* </ul>
9374		*@version 2010 January 18
9375		*
9376		* @since Release 20101201
9377		*
9378		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9379		*/
9380		public static double[] jauGd2gc ( int n, double elong, double phi, double height ) throws JSOFAIllegalParameter, JSOFAInternalError
9381		{
9382
9383
9384		/* Obtain reference ellipsoid parameters. */
9385	40	ReferenceEllipsoid em = jauEform ( n );
9386
9387		/* If OK, transform longitude, geodetic latitude, height to x,y,z. */
9388	36	return jauGd2gce ( em.a, em.f, elong, phi, height );
9389
9390
9391		}
9392
9393
9394		/**
9395		* Transform geodetic coordinates to geocentric for a reference
9396		* ellipsoid of specified form.
9397		*
9398		*<p>This function is derived from the International Astronomical Union's
9399		* JSOFA (Standards of Fundamental Astronomy) software collection.
9400		*
9401		*<p>Status: support function.
9402		*
9403		*<!-- Given: -->
9404		* @param a double equatorial radius (Notes 1,4)
9405		* @param f double flattening (Notes 2,4)
9406		* @param elong double longitude (radians, east +ve)
9407		* @param phi double latitude (geodetic, radians, Note 4)
9408		* @param height double height above ellipsoid (geodetic, Notes 3,4)
9409		*
9410		*<!-- Returned: -->
9411		* @return xyz double[3] <u>returned</u> geocentric vector (Note 3)
9412		*
9413		* <!-- Returned (function value): -->
9414		* @throws JSOFAInternalError
9415		* 0 = OK
9416		* -1 = illegal case (Note 4)
9417		* <p>Notes:
9418		* <ol>
9419		*
9420		* <li> The equatorial radius, a, can be in any units, but meters is
9421		* the conventional choice.
9422		*
9423		* <li> The flattening, f, is (for the Earth) a value around 0.00335,
9424		* i.e. around 1/298.
9425		*
9426		* <li> The equatorial radius, a, and the height, height, must be
9427		* given in the same units, and determine the units of the
9428		* returned geocentric vector, xyz.
9429		*
9430		* <li> No validation is performed on individual arguments. The error
9431		* status -1 protects against (unrealistic) cases that would lead
9432		* to arithmetic exceptions. If an error occurs, xyz is unchanged.
9433		*
9434		* <li> The inverse transformation is performed in the function
9435		* jauGc2gde.
9436		*
9437		* <li> The transformation for a standard ellipsoid (such as WGS84) can
9438		* more conveniently be performed by calling jauGd2gc, which uses a
9439		* numerical code (1 for WGS84) to identify the required a and f
9440		* values.
9441		*</ol>
9442		*<p>References:
9443		*
9444		* <p>Green, R.M., Spherical Astronomy, Cambridge University Press,
9445		* (1985) Section 4.5, p96.
9446		*
9447		* <p>Explanatory Supplement to the Astronomical Almanac,
9448		* P. Kenneth Seidelmann (ed), University Science Books (1992),
9449		* Section 4.22, p202.
9450		*
9451		*@version 2009 November 2
9452		*
9453		* @since Release 20101201
9454		*
9455		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9456		*/
9457		public static double[] jauGd2gce ( double a, double f, double elong, double phi,
9458		double height ) throws JSOFAInternalError
9459		{
9460		double sp, cp, w, d, ac, as, r;
9461	38	double xyz[] = new double[3];
9462
9463
9464		/* Functions of geodetic latitude. */
9465	38	sp = sin(phi);
9466	38	cp = cos(phi);
9467	38	w = 1.0 - f;
9468	38	w = w * w;
9469	38	d = cpcp + wsp*sp;
9470	38	if ( d <= 0.0 ) throw new JSOFAInternalError("illegal combination of arguments d< 0", -1);
9471	38	ac = a / sqrt(d);
9472	38	as = w * ac;
9473
9474		/* Geocentric vector. */
9475	38	r = (ac + height) * cp;
9476	38	xyz[0] = r * cos(elong);
9477	38	xyz[1] = r * sin(elong);
9478	38	xyz[2] = (as + height) * sp;
9479
9480		/* Success. */
9481	38	return xyz;
9482
9483
9484		}
9485
9486
9487		/**
9488		* Greenwich mean sidereal time (model consistent with IAU 2000
9489		* resolutions).
9490		*
9491		*<p>This function is derived from the International Astronomical Union's
9492		* SOFA (Standards Of Fundamental Astronomy) software collection.
9493		*
9494		*<p>Status: canonical model.
9495		*
9496		*<!-- Given: -->
9497		* @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9498		* @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9499		* @param tta double TT as a 2-part Julian Date (Notes 1,2)
9500		* @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9501		*
9502		* <!-- Returned (function value): -->
9503		* @return double Greenwich mean sidereal time (radians)
9504		*
9505		* <p>Notes:
9506		* <ol>
9507		*
9508		* <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9509		* Julian Dates, apportioned in any convenient way between the
9510		* argument pairs. For example, JD=2450123.7 could be expressed in
9511		* any of these ways, among others:
9512		*<pre>
9513		* Part A Part B
9514		*
9515		* 2450123.7 0.0 (JD method)
9516		* 2451545.0 -1421.3 (J2000 method)
9517		* 2400000.5 50123.2 (MJD method)
9518		* 2450123.5 0.2 (date & time method)
9519		*</pre>
9520		* The JD method is the most natural and convenient to use in
9521		* cases where the loss of several decimal digits of resolution
9522		* is acceptable (in the case of UT; the TT is not at all critical
9523		* in this respect). The J2000 and MJD methods are good compromises
9524		* between resolution and convenience. For UT, the date & time
9525		* method is best matched to the algorithm that is used by the Earth
9526		* Rotation Angle function, called internally: maximum precision is
9527		* delivered when the uta argument is for 0hrs UT1 on the day in
9528		* question and the utb argument lies in the range 0 to 1, or vice
9529		* versa.
9530		*
9531		* <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
9532		* and TT to predict the effects of precession. If UT1 is used for
9533		* both purposes, errors of order 100 microarcseconds result.
9534		*
9535		* <li> This GMST is compatible with the IAU 2000 resolutions and must be
9536		* used only in conjunction with other IAU 2000 compatible
9537		* components such as precession-nutation and equation of the
9538		* equinoxes.
9539		*
9540		* <li> The result is returned in the range 0 to 2pi.
9541		*
9542		* <li> The algorithm is from Capitaine et al. (2003) and IERS
9543		* Conventions 2003.
9544		*</ol>
9545		*<p>Called:<ul>
9546		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
9547		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9548		* </ul>
9549		*<p>References:
9550		*
9551		* <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
9552		* implement the IAU 2000 definition of UT1", Astronomy &
9553		* Astrophysics, 406, 1135-1149 (2003)
9554		*
9555		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
9556		* IERS Technical Note No. 32, BKG (2004)
9557		*
9558		*@version 2009 March 16
9559		*
9560		* @since Release 20101201
9561		*
9562		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9563		*/
9564		public static double jauGmst00(double uta, double utb, double tta, double ttb)
9565		{
9566		double t, gmst;
9567
9568
9569		/* TT Julian centuries since J2000.0. */
9570	8	t = ((tta - DJ00) + ttb) / DJC;
9571
9572		/* Greenwich Mean Sidereal Time, IAU 2000. */
9573	8	gmst = jauAnp(jauEra00(uta, utb) +
9574		( 0.014506 +
9575		( 4612.15739966 +
9576		( 1.39667721 +
9577		( -0.00009344 +
9578		( 0.00001882 )
9579		* t) * t) * t) * t) * DAS2R);
9580
9581	8	return gmst;
9582
9583		}
9584
9585
9586		/**
9587		* Greenwich mean sidereal time (consistent with IAU 2006 precession).
9588		*
9589		*<p>This function is derived from the International Astronomical Union's
9590		* SOFA (Standards Of Fundamental Astronomy) software collection.
9591		*
9592		*<p>Status: canonical model.
9593		*
9594		*<!-- Given: -->
9595		* @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9596		* @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9597		* @param tta double TT as a 2-part Julian Date (Notes 1,2)
9598		* @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9599		*
9600		* <!-- Returned (function value): -->
9601		* @return double Greenwich mean sidereal time (radians)
9602		*
9603		* <p>Notes:
9604		* <ol>
9605		*
9606		* <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9607		* Julian Dates, apportioned in any convenient way between the
9608		* argument pairs. For example, JD=2450123.7 could be expressed in
9609		* any of these ways, among others:
9610		*<pre>
9611		* Part A Part B
9612		*
9613		* 2450123.7 0.0 (JD method)
9614		* 2451545.0 -1421.3 (J2000 method)
9615		* 2400000.5 50123.2 (MJD method)
9616		* 2450123.5 0.2 (date & time method)
9617		*</pre>
9618		* The JD method is the most natural and convenient to use in
9619		* cases where the loss of several decimal digits of resolution
9620		* is acceptable (in the case of UT; the TT is not at all critical
9621		* in this respect). The J2000 and MJD methods are good compromises
9622		* between resolution and convenience. For UT, the date & time
9623		* method is best matched to the algorithm that is used by the Earth
9624		* rotation angle function, called internally: maximum precision is
9625		* delivered when the uta argument is for 0hrs UT1 on the day in
9626		* question and the utb argument lies in the range 0 to 1, or vice
9627		* versa.
9628		*
9629		* <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
9630		* and TT to predict the effects of precession. If UT1 is used for
9631		* both purposes, errors of order 100 microarcseconds result.
9632		*
9633		* <li> This GMST is compatible with the IAU 2006 precession and must not
9634		* be used with other precession models.
9635		*
9636		* <li> The result is returned in the range 0 to 2pi.
9637		*</ol>
9638		*<p>Called:<ul>
9639		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
9640		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9641		* </ul>
9642		*<p>Reference:
9643		*
9644		* <p>Capitaine, N., Wallace, P.T. & Chapront, J., 2005,
9645		* Astron.Astrophys. 432, 355
9646		*
9647		*@version 2008 May 24
9648		*
9649		* @since Release 20101201
9650		*
9651		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9652		*/
9653		public static double jauGmst06(double uta, double utb, double tta, double ttb)
9654		{
9655		double t, gmst;
9656
9657
9658		/* TT Julian centuries since J2000.0. */
9659	4	t = ((tta - DJ00) + ttb) / DJC;
9660
9661		/* Greenwich mean sidereal time, IAU 2006. */
9662	4	gmst = jauAnp(jauEra00(uta, utb) +
9663		( 0.014506 +
9664		( 4612.156534 +
9665		( 1.3915817 +
9666		( -0.00000044 +
9667		( -0.000029956 +
9668		( -0.0000000368 )
9669		* t) * t) * t) * t) * t) * DAS2R);
9670
9671	4	return gmst;
9672
9673		}
9674
9675
9676		/**
9677		* Universal Time to Greenwich mean sidereal time (IAU 1982 model).
9678		*
9679		*<p>This function is derived from the International Astronomical Union's
9680		* SOFA (Standards Of Fundamental Astronomy) software collection.
9681		*
9682		*<p>Status: canonical model.
9683		*
9684		*<!-- Given: -->
9685		* @param dj1 double UT1 Julian Date (see note)
9686		* @param dj2 double UT1 Julian Date (see note)
9687		*
9688		* <!-- Returned (function value): -->
9689		* @return double Greenwich mean sidereal time (radians)
9690		*
9691		* <p>Notes:
9692		* <ol>
9693		*
9694		* <li> The UT1 date dj1+dj2 is a Julian Date, apportioned in any
9695		* convenient way between the arguments dj1 and dj2. For example,
9696		* JD(UT1)=2450123.7 could be expressed in any of these ways,
9697		* among others:
9698		*<pre>
9699		* dj1 dj2
9700		*
9701		* 2450123.7D0 0D0 (JD method)
9702		* 2451545D0 -1421.3D0 (J2000 method)
9703		* 2400000.5D0 50123.2D0 (MJD method)
9704		* 2450123.5D0 0.2D0 (date & time method)
9705		*</pre>
9706		* The JD method is the most natural and convenient to use in
9707		* cases where the loss of several decimal digits of resolution
9708		* is acceptable. The J2000 and MJD methods are good compromises
9709		* between resolution and convenience. The date & time method is
9710		* best matched to the algorithm used: maximum accuracy (or, at
9711		* least, minimum noise) is delivered when the dj1 argument is for
9712		* 0hrs UT1 on the day in question and the dj2 argument lies in the
9713		* range 0 to 1, or vice versa.
9714		*
9715		* <li> The algorithm is based on the IAU 1982 expression. This is
9716		* always described as giving the GMST at 0 hours UT1. In fact, it
9717		* gives the difference between the GMST and the UT, the steady
9718		* 4-minutes-per-day drawing-ahead of ST with respect to UT. When
9719		* whole days are ignored, the expression happens to equal the GMST
9720		* at 0 hours UT1 each day.
9721		*
9722		* <li> In this function, the entire UT1 (the sum of the two arguments
9723		* dj1 and dj2) is used directly as the argument for the standard
9724		* formula, the constant term of which is adjusted by 12 hours to
9725		* take account of the noon phasing of Julian Date. The UT1 is then
9726		* added, but omitting whole days to conserve accuracy.
9727		*</ol>
9728		*<p>Called:<ul>
9729		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9730		* </ul>
9731		*<p>References:
9732		*
9733		* <p>Transactions of the International Astronomical Union,
9734		* XVIII B, 67 (1983).
9735		*
9736		* <p>Aoki et al., Astron. Astrophys. 105, 359-361 (1982).
9737		*
9738		*@version 2008 May 24
9739		*
9740		* @since Release 20101201
9741		*
9742		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9743		*/
9744		public static double jauGmst82(double dj1, double dj2)
9745		{
9746		/* Coefficients of IAU 1982 GMST-UT1 model */
9747	4	double A = 24110.54841 - DAYSEC / 2.0;
9748	4	double B = 8640184.812866;
9749	4	double C = 0.093104;
9750	4	double D = -6.2e-6;
9751
9752		/* Note: the first constant, A, has to be adjusted by 12 hours */
9753		/* because the UT1 is supplied as a Julian date, which begins */
9754		/* at noon. */
9755
9756		double d1, d2, t, f, gmst;
9757
9758
9759		/* Julian centuries since fundamental epoch. */
9760	4	if (dj1 < dj2) {
9761	0	d1 = dj1;
9762	0	d2 = dj2;
9763		} else {
9764	4	d1 = dj2;
9765	4	d2 = dj1;
9766		}
9767	4	t = (d1 + (d2 - DJ00)) / DJC;
9768
9769		/* Fractional part of JD(UT1), in seconds. */
9770	4	f = DAYSEC * (fmod(d1, 1.0) + fmod(d2, 1.0));
9771
9772		/* GMST at this UT1. */
9773	4	gmst = jauAnp(DS2R * ((A + (B + (C + D * t) * t) * t) + f));
9774
9775	4	return gmst;
9776
9777		}
9778
9779
9780		/**
9781		* Greenwich apparent sidereal time (consistent with IAU 2000
9782		* resolutions).
9783		*
9784		*<p>This function is derived from the International Astronomical Union's
9785		* SOFA (Standards Of Fundamental Astronomy) software collection.
9786		*
9787		*<p>Status: canonical model.
9788		*
9789		*<!-- Given: -->
9790		* @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9791		* @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9792		* @param tta double TT as a 2-part Julian Date (Notes 1,2)
9793		* @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9794		*
9795		* <!-- Returned (function value): -->
9796		* @return double Greenwich apparent sidereal time (radians)
9797		*
9798		* <p>Notes:
9799		* <ol>
9800		*
9801		* <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9802		* Julian Dates, apportioned in any convenient way between the
9803		* argument pairs. For example, JD=2450123.7 could be expressed in
9804		* any of these ways, among others:
9805		*<pre>
9806		* Part A Part B
9807		*
9808		* 2450123.7 0.0 (JD method)
9809		* 2451545.0 -1421.3 (J2000 method)
9810		* 2400000.5 50123.2 (MJD method)
9811		* 2450123.5 0.2 (date & time method)
9812		*</pre>
9813		* The JD method is the most natural and convenient to use in
9814		* cases where the loss of several decimal digits of resolution
9815		* is acceptable (in the case of UT; the TT is not at all critical
9816		* in this respect). The J2000 and MJD methods are good compromises
9817		* between resolution and convenience. For UT, the date & time
9818		* method is best matched to the algorithm that is used by the Earth
9819		* Rotation Angle function, called internally: maximum precision is
9820		* delivered when the uta argument is for 0hrs UT1 on the day in
9821		* question and the utb argument lies in the range 0 to 1, or vice
9822		* versa.
9823		*
9824		* <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
9825		* and TT to predict the effects of precession-nutation. If UT1 is
9826		* used for both purposes, errors of order 100 microarcseconds
9827		* result.
9828		*
9829		* <li> This GAST is compatible with the IAU 2000 resolutions and must be
9830		* used only in conjunction with other IAU 2000 compatible
9831		* components such as precession-nutation.
9832		*
9833		* <li> The result is returned in the range 0 to 2pi.
9834		*
9835		* <li> The algorithm is from Capitaine et al. (2003) and IERS
9836		* Conventions 2003.
9837		*</ol>
9838		*<p>Called:<ul>
9839		* <li>{@link #jauGmst00} Greenwich mean sidereal time, IAU 2000
9840		* <li>{@link #jauEe00a} equation of the equinoxes, IAU 2000A
9841		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9842		* </ul>
9843		*<p>References:
9844		*
9845		* <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
9846		* implement the IAU 2000 definition of UT1", Astronomy &
9847		* Astrophysics, 406, 1135-1149 (2003)
9848		*
9849		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
9850		* IERS Technical Note No. 32, BKG (2004)
9851		*
9852		*@version 2008 May 16
9853		*
9854		* @since Release 20101201
9855		*
9856		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9857		*/
9858		public static double jauGst00a(double uta, double utb, double tta, double ttb)
9859		{
9860		double gmst00, ee00a, gst;
9861
9862
9863	2	gmst00 = jauGmst00(uta, utb, tta, ttb);
9864	2	ee00a = jauEe00a(tta, ttb);
9865	2	gst = jauAnp(gmst00 + ee00a);
9866
9867	2	return gst;
9868
9869		}
9870
9871
9872		/**
9873		* Greenwich apparent sidereal time (consistent with IAU 2000
9874		* resolutions but using the truncated nutation model IAU 2000B).
9875		*
9876		*<p>This function is derived from the International Astronomical Union's
9877		* SOFA (Standards Of Fundamental Astronomy) software collection.
9878		*
9879		*<p>Status: support function.
9880		*
9881		*<!-- Given: -->
9882		* @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9883		* @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9884		*
9885		* <!-- Returned (function value): -->
9886		* @return double Greenwich apparent sidereal time (radians)
9887		*
9888		* <p>Notes:
9889		* <ol>
9890		*
9891		* <li> The UT1 date uta+utb is a Julian Date, apportioned in any
9892		* convenient way between the argument pair. For example,
9893		* JD=2450123.7 could be expressed in any of these ways, among
9894		* others:
9895		*<pre>
9896		* uta utb
9897		*
9898		* 2450123.7 0.0 (JD method)
9899		* 2451545.0 -1421.3 (J2000 method)
9900		* 2400000.5 50123.2 (MJD method)
9901		* 2450123.5 0.2 (date & time method)
9902		*</pre>
9903		* The JD method is the most natural and convenient to use in cases
9904		* where the loss of several decimal digits of resolution is
9905		* acceptable. The J2000 and MJD methods are good compromises
9906		* between resolution and convenience. For UT, the date & time
9907		* method is best matched to the algorithm that is used by the Earth
9908		* Rotation Angle function, called internally: maximum precision is
9909		* delivered when the uta argument is for 0hrs UT1 on the day in
9910		* question and the utb argument lies in the range 0 to 1, or vice
9911		* versa.
9912		*
9913		* <li> The result is compatible with the IAU 2000 resolutions, except
9914		* that accuracy has been compromised for the sake of speed and
9915		* convenience in two respects:
9916		*
9917		* . UT is used instead of TDB (or TT) to compute the precession
9918		* component of GMST and the equation of the equinoxes. This
9919		* results in errors of order 0.1 mas at present.
9920		*
9921		* . The IAU 2000B abridged nutation model (McCarthy & Luzum, 2001)
9922		* is used, introducing errors of up to 1 mas.
9923		*
9924		* <li> This GAST is compatible with the IAU 2000 resolutions and must be
9925		* used only in conjunction with other IAU 2000 compatible
9926		* components such as precession-nutation.
9927		*
9928		* <li> The result is returned in the range 0 to 2pi.
9929		*
9930		* <li> The algorithm is from Capitaine et al. (2003) and IERS
9931		* Conventions 2003.
9932		*</ol>
9933		*<p>Called:<ul>
9934		* <li>{@link #jauGmst00} Greenwich mean sidereal time, IAU 2000
9935		* <li>{@link #jauEe00b} equation of the equinoxes, IAU 2000B
9936		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
9937		* </ul>
9938		*<p>References:
9939		*
9940		* <p>Capitaine, N., Wallace, P.T. and McCarthy, D.D., "Expressions to
9941		* implement the IAU 2000 definition of UT1", Astronomy &
9942		* Astrophysics, 406, 1135-1149 (2003)
9943		*
9944		* <p>McCarthy, D.D. & Luzum, B.J., "An abridged model of the
9945		* precession-nutation of the celestial pole", Celestial Mechanics &
9946		* Dynamical Astronomy, 85, 37-49 (2003)
9947		*
9948		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
9949		* IERS Technical Note No. 32, BKG (2004)
9950		*
9951		*@version 2008 May 16
9952		*
9953		* @since Release 20101201
9954		*
9955		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
9956		*/
9957		public static double jauGst00b(double uta, double utb)
9958		{
9959		double gmst00, ee00b, gst;
9960
9961
9962	2	gmst00 = jauGmst00(uta, utb, uta, utb);
9963	2	ee00b = jauEe00b(uta, utb);
9964	2	gst = jauAnp(gmst00 + ee00b);
9965
9966	2	return gst;
9967
9968		}
9969
9970
9971		/**
9972		* Greenwich apparent sidereal time, IAU 2006, given the NPB matrix.
9973		*
9974		*<p>This function is derived from the International Astronomical Union's
9975		* SOFA (Standards Of Fundamental Astronomy) software collection.
9976		*
9977		*<p>Status: support function.
9978		*
9979		*<!-- Given: -->
9980		* @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
9981		* @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
9982		* @param tta double TT as a 2-part Julian Date (Notes 1,2)
9983		* @param ttb double TT as a 2-part Julian Date (Notes 1,2)
9984		* @param rnpb double[3][3] nutation x precession x bias matrix
9985		*
9986		* <!-- Returned (function value): -->
9987		* @return double Greenwich apparent sidereal time (radians)
9988		*
9989		* <p>Notes:
9990		* <ol>
9991		*
9992		* <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
9993		* Julian Dates, apportioned in any convenient way between the
9994		* argument pairs. For example, JD=2450123.7 could be expressed in
9995		* any of these ways, among others:
9996		*<pre>
9997		* Part A Part B
9998		*
9999		* 2450123.7 0.0 (JD method)
10000		* 2451545.0 -1421.3 (J2000 method)
10001		* 2400000.5 50123.2 (MJD method)
10002		* 2450123.5 0.2 (date & time method)
10003		*</pre>
10004		* The JD method is the most natural and convenient to use in
10005		* cases where the loss of several decimal digits of resolution
10006		* is acceptable (in the case of UT; the TT is not at all critical
10007		* in this respect). The J2000 and MJD methods are good compromises
10008		* between resolution and convenience. For UT, the date & time
10009		* method is best matched to the algorithm that is used by the Earth
10010		* rotation angle function, called internally: maximum precision is
10011		* delivered when the uta argument is for 0hrs UT1 on the day in
10012		* question and the utb argument lies in the range 0 to 1, or vice
10013		* versa.
10014		*
10015		* <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
10016		* and TT to predict the effects of precession-nutation. If UT1 is
10017		* used for both purposes, errors of order 100 microarcseconds
10018		* result.
10019		*
10020		* <li> Although the function uses the IAU 2006 series for s+XY/2, it is
10021		* otherwise independent of the precession-nutation model and can in
10022		* practice be used with any equinox-based NPB matrix.
10023		*
10024		* <li> The result is returned in the range 0 to 2pi.
10025		*</ol>
10026		*<p>Called:<ul>
10027		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
10028		* <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
10029		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
10030		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
10031		* <li>{@link #jauEors} equation of the origins, given NPB matrix and s
10032		* </ul>
10033		*<p>Reference:
10034		*
10035		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
10036		*
10037		*@version 2008 May 24
10038		*
10039		* @since Release 20101201
10040		*
10041		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10042		*/
10043		public static double jauGst06(double uta, double utb, double tta, double ttb,
10044		double rnpb[][])
10045		{
10046		double s, era, eors, gst;
10047
10048
10049		/* Extract CIP coordinates. */
10050	6	CelestialIntermediatePole cip = jauBpn2xy(rnpb);
10051
10052		/* The CIO locator, s. */
10053	6	s = jauS06(tta, ttb, cip.x, cip.y);
10054
10055		/* Greenwich apparent sidereal time. */
10056	6	era = jauEra00(uta, utb);
10057	6	eors = jauEors(rnpb, s);
10058	6	gst = jauAnp(era - eors);
10059
10060	6	return gst;
10061
10062		}
10063
10064
10065		/**
10066		* Greenwich apparent sidereal time (consistent with IAU 2000 and 2006
10067		* resolutions).
10068		*
10069		*<p>This function is derived from the International Astronomical Union's
10070		* SOFA (Standards Of Fundamental Astronomy) software collection.
10071		*
10072		*<p>Status: canonical model.
10073		*
10074		*<!-- Given: -->
10075		* @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
10076		* @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
10077		* @param tta double TT as a 2-part Julian Date (Notes 1,2)
10078		* @param ttb double TT as a 2-part Julian Date (Notes 1,2)
10079		*
10080		* <!-- Returned (function value): -->
10081		* @return double Greenwich apparent sidereal time (radians)
10082		*
10083		* <p>Notes:
10084		* <ol>
10085		*
10086		* <li> The UT1 and TT dates uta+utb and tta+ttb respectively, are both
10087		* Julian Dates, apportioned in any convenient way between the
10088		* argument pairs. For example, JD=2450123.7 could be expressed in
10089		* any of these ways, among others:
10090		*<pre>
10091		* Part A Part B
10092		*
10093		* 2450123.7 0.0 (JD method)
10094		* 2451545.0 -1421.3 (J2000 method)
10095		* 2400000.5 50123.2 (MJD method)
10096		* 2450123.5 0.2 (date & time method)
10097		*</pre>
10098		* The JD method is the most natural and convenient to use in
10099		* cases where the loss of several decimal digits of resolution
10100		* is acceptable (in the case of UT; the TT is not at all critical
10101		* in this respect). The J2000 and MJD methods are good compromises
10102		* between resolution and convenience. For UT, the date & time
10103		* method is best matched to the algorithm that is used by the Earth
10104		* rotation angle function, called internally: maximum precision is
10105		* delivered when the uta argument is for 0hrs UT1 on the day in
10106		* question and the utb argument lies in the range 0 to 1, or vice
10107		* versa.
10108		*
10109		* <li> Both UT1 and TT are required, UT1 to predict the Earth rotation
10110		* and TT to predict the effects of precession-nutation. If UT1 is
10111		* used for both purposes, errors of order 100 microarcseconds
10112		* result.
10113		*
10114		* <li> This GAST is compatible with the IAU 2000/2006 resolutions and
10115		* must be used only in conjunction with IAU 2006 precession and
10116		* IAU 2000A nutation.
10117		*
10118		* <li> The result is returned in the range 0 to 2pi.
10119		*</ol>
10120		*<p>Called:<ul>
10121		* <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
10122		* <li>{@link #jauGst06} Greenwich apparent ST, IAU 2006, given NPB matrix
10123		* </ul>
10124		*<p>Reference:
10125		*
10126		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
10127		*
10128		*@version 2008 May 16
10129		*
10130		* @since Release 20101201
10131		*
10132		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10133		*/
10134		public static double jauGst06a(double uta, double utb, double tta, double ttb)
10135		{
10136	4	double rnpb[][] = new double[3][3], gst;
10137
10138
10139		/* Classical nutation x precession x bias matrix, IAU 2000A. */
10140	4	rnpb = jauPnm06a(tta, ttb);
10141
10142		/* Greenwich apparent sidereal time. */
10143	4	gst = jauGst06(uta, utb, tta, ttb, rnpb);
10144
10145	4	return gst;
10146
10147		}
10148
10149
10150		/**
10151		* Greenwich apparent sidereal time (consistent with IAU 1982/94
10152		* resolutions).
10153		*
10154		*<p>This function is derived from the International Astronomical Union's
10155		* SOFA (Standards Of Fundamental Astronomy) software collection.
10156		*
10157		*<p>Status: support function.
10158		*
10159		*<!-- Given: -->
10160		* @param uta double UT1 as a 2-part Julian Date (Notes 1,2)
10161		* @param utb double UT1 as a 2-part Julian Date (Notes 1,2)
10162		*
10163		* <!-- Returned (function value): -->
10164		* @return double Greenwich apparent sidereal time (radians)
10165		*
10166		* <p>Notes:
10167		* <ol>
10168		*
10169		* <li> The UT1 date uta+utb is a Julian Date, apportioned in any
10170		* convenient way between the argument pair. For example,
10171		* JD=2450123.7 could be expressed in any of these ways, among
10172		* others:
10173		*<pre>
10174		* uta utb
10175		*
10176		* 2450123.7 0.0 (JD method)
10177		* 2451545.0 -1421.3 (J2000 method)
10178		* 2400000.5 50123.2 (MJD method)
10179		* 2450123.5 0.2 (date & time method)
10180		*</pre>
10181		* The JD method is the most natural and convenient to use in cases
10182		* where the loss of several decimal digits of resolution is
10183		* acceptable. The J2000 and MJD methods are good compromises
10184		* between resolution and convenience. For UT, the date & time
10185		* method is best matched to the algorithm that is used by the Earth
10186		* Rotation Angle function, called internally: maximum precision is
10187		* delivered when the uta argument is for 0hrs UT1 on the day in
10188		* question and the utb argument lies in the range 0 to 1, or vice
10189		* versa.
10190		*
10191		* <li> The result is compatible with the IAU 1982 and 1994 resolutions,
10192		* except that accuracy has been compromised for the sake of
10193		* convenience in that UT is used instead of TDB (or TT) to compute
10194		* the equation of the equinoxes.
10195		*
10196		* <li> This GAST must be used only in conjunction with contemporaneous
10197		* IAU standards such as 1976 precession, 1980 obliquity and 1982
10198		* nutation. It is not compatible with the IAU 2000 resolutions.
10199		*
10200		* <li> The result is returned in the range 0 to 2pi.
10201		*</ol>
10202		*<p>Called:<ul>
10203		* <li>{@link #jauGmst82} Greenwich mean sidereal time, IAU 1982
10204		* <li>{@link #jauEqeq94} equation of the equinoxes, IAU 1994
10205		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
10206		* </ul>
10207		*<p>References:
10208		*
10209		* <p>Explanatory Supplement to the Astronomical Almanac,
10210		* P. Kenneth Seidelmann (ed), University Science Books (1992)
10211		*
10212		* IAU Resolution C7, Recommendation 3 (1994)
10213		*
10214		*@version 2008 May 16
10215		*
10216		* @since Release 20101201
10217		*
10218		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10219		*/
10220		public static double jauGst94(double uta, double utb)
10221		{
10222		double gmst82, eqeq94, gst;
10223
10224
10225	2	gmst82 = jauGmst82(uta, utb);
10226	2	eqeq94 = jauEqeq94(uta, utb);
10227	2	gst = jauAnp(gmst82 + eqeq94);
10228
10229	2	return gst;
10230
10231		}
10232
10233
10234		/**
10235		* Transform Hipparcos star data into the FK5 (J2000.0) system.
10236		*
10237		*<p>This function is derived from the International Astronomical Union's
10238		* SOFA (Standards Of Fundamental Astronomy) software collection.
10239		*
10240		*<p>Status: support function.
10241		*
10242		* Given (all Hipparcos, epoch J2000.0):
10243		* rh double RA (radians)
10244		* dh double Dec (radians)
10245		* drh double proper motion in RA (dRA/dt, rad/Jyear)
10246		* ddh double proper motion in Dec (dDec/dt, rad/Jyear)
10247		* pxh double parallax (arcsec)
10248		* rvh double radial velocity (km/s, positive = receding)
10249		*
10250		* Returned (all FK5, equinox J2000.0, epoch J2000.0):
10251		* r5 double RA (radians)
10252		* d5 double Dec (radians)
10253		* dr5 double proper motion in RA (dRA/dt, rad/Jyear)
10254		* dd5 double proper motion in Dec (dDec/dt, rad/Jyear)
10255		* px5 double parallax (arcsec)
10256		* rv5 double radial velocity (km/s, positive = receding)
10257		*
10258		* <p>Notes:
10259		* <ol>
10260		*
10261		* <li> This function transforms Hipparcos star positions and proper
10262		* motions into FK5 J2000.0.
10263		*
10264		* <li> The proper motions in RA are dRA/dt rather than
10265		* cos(Dec)*dRA/dt, and are per year rather than per century.
10266		*
10267		* <li> The FK5 to Hipparcos transformation is modeled as a pure
10268		* rotation and spin; zonal errors in the FK5 catalog are not
10269		* taken into account.
10270		*
10271		* <li> See also jauFk52h, jauFk5hz, jauHfk5z.
10272		*</ol>
10273		*<p>Called:<ul>
10274		* <li>{@link #jauStarpv} star catalog data to space motion pv-vector
10275		* <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
10276		* <li>{@link #jauRv2m} r-vector to r-matrix
10277		* <li>{@link #jauRxp} product of r-matrix and p-vector
10278		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
10279		* <li>{@link #jauPxp} vector product of two p-vectors
10280		* <li>{@link #jauPmp} p-vector minus p-vector
10281		* <li>{@link #jauPvstar} space motion pv-vector to star catalog data
10282		* </ul>
10283		*<p>Reference:
10284		*
10285		* <p>F.Mignard & M.Froeschle, Astron. Astrophys. 354, 732-739 (2000).
10286		*
10287		*@version 2009 December 17
10288		*
10289		* @since Release 20101201
10290		*
10291		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10292		*/
10293		public static CatalogCoords jauH2fk5(double rh, double dh,
10294		double drh, double ddh, double pxh, double rvh)
10295		{
10296		int i;
10297	2	double pvh[][] = new double[2][3], r5h[][] = new double[3][3], s5h[] = new double[3], sh[] = new double[3], wxp[] = new double[3], vv[] = new double[3], pv5[][] = new double[2][3];
10298
10299
10300		/* Hipparcos barycentric position/velocity pv-vector (normalized). */
10301	2	jauStarpv(rh, dh, drh, ddh, pxh, rvh, pvh);
10302
10303		/* FK5 to Hipparcos orientation matrix and spin vector. */
10304	2	jauFk5hip(r5h, s5h);
10305
10306		/* Make spin units per day instead of per year. */
10307	2	for ( i = 0; i < 3; s5h[i++] /= 365.25 );
10308
10309		/* Orient the spin into the Hipparcos system. */
10310	2	sh = jauRxp(r5h, s5h);
10311
10312		/* De-orient the Hipparcos position into the FK5 system. */
10313	2	pv5[0] = jauTrxp(r5h, pvh[0]);
10314
10315		/* Apply spin to the position giving an extra space motion component. */
10316	2	wxp = jauPxp(pvh[0],sh);
10317
10318		/* Subtract this component from the Hipparcos space motion. */
10319	2	vv = jauPmp(pvh[1], wxp);
10320
10321		/* De-orient the Hipparcos space motion into the FK5 system. */
10322	2	pv5[1] = jauTrxp(r5h, vv);
10323
10324		/* FK5 pv-vector to spherical., r5, d5, dr5, dd5, px5, rv5 */
10325	2	CatalogCoords cat = null;
10326		try {
10327	2	cat = jauPvstar(pv5);
10328	0	} catch (JSOFAInternalError e) {
10329		// original code just ignored this possibility
10330	0	e.printStackTrace();
10331	2	}
10332
10333	2	return cat;
10334
10335		}
10336
10337
10338		/**
10339		* Transform a Hipparcos star position into FK5 J2000.0, assuming
10340		* zero Hipparcos proper motion.
10341		*
10342		*<p>This function is derived from the International Astronomical Union's
10343		* SOFA (Standards Of Fundamental Astronomy) software collection.
10344		*
10345		*<p>Status: support function.
10346		*
10347		*<!-- Given: -->
10348		* @param rh double Hipparcos RA (radians)
10349		* @param dh double Hipparcos Dec (radians)
10350		* @param date1 double TDB date (Note 1)
10351		* @param date2 double TDB date (Note 1)
10352		*
10353		* FIXME original did not return the parallax and radial velocity of the CatalogCoords type.
10354		* Returned (all FK5, equinox J2000.0, date date1+date2):
10355		* r5 double RA (radians)
10356		* d5 double Dec (radians)
10357		* dr5 double FK5 RA proper motion (rad/year, Note 4)
10358		* dd5 double Dec proper motion (rad/year, Note 4)
10359		*
10360		* <p>Notes:
10361		* <ol>
10362		*
10363		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
10364		* convenient way between the two arguments. For example,
10365		* JD(TT)=2450123.7 could be expressed in any of these ways,
10366		* among others:
10367		*<pre>
10368		* date1 date2
10369		*
10370		* 2450123.7 0.0 (JD method)
10371		* 2451545.0 -1421.3 (J2000 method)
10372		* 2400000.5 50123.2 (MJD method)
10373		* 2450123.5 0.2 (date & time method)
10374		*</pre>
10375		* The JD method is the most natural and convenient to use in
10376		* cases where the loss of several decimal digits of resolution
10377		* is acceptable. The J2000 method is best matched to the way
10378		* the argument is handled internally and will deliver the
10379		* optimum resolution. The MJD method and the date & time methods
10380		* are both good compromises between resolution and convenience.
10381		*
10382		* <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
10383		*
10384		* <li> The FK5 to Hipparcos transformation is modeled as a pure rotation
10385		* and spin; zonal errors in the FK5 catalogue are not taken into
10386		* account.
10387		*
10388		* <li> It was the intention that Hipparcos should be a close
10389		* approximation to an inertial frame, so that distant objects have
10390		* zero proper motion; such objects have (in general) non-zero
10391		* proper motion in FK5, and this function returns those fictitious
10392		* proper motions.
10393		*
10394		* <li> The position returned by this function is in the FK5 J2000.0
10395		* reference system but at date date1+date2.
10396		*
10397		* <li> See also jauFk52h, jauH2fk5, jauFk5zhz.
10398		*</ol>
10399		*<p>Called:<ul>
10400		* <li>{@link #jauS2c} spherical coordinates to unit vector
10401		* <li>{@link #jauFk5hip} FK5 to Hipparcos rotation and spin
10402		* <li>{@link #jauRxp} product of r-matrix and p-vector
10403		* <li>{@link #jauSxp} multiply p-vector by scalar
10404		* <li>{@link #jauRxr} product of two r-matrices
10405		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
10406		* <li>{@link #jauPxp} vector product of two p-vectors
10407		* <li>{@link #jauPv2s} pv-vector to spherical
10408		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
10409		* </ul>
10410		*<p>Reference:
10411		*
10412		* <p>F.Mignard & M.Froeschle, 2000, Astron.Astrophys. 354, 732-739.
10413		*
10414		*@version 2009 December 17
10415		*
10416		* @since Release 20101201
10417		*
10418		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10419		*
10420		*/
10421		public static CatalogCoords jauHfk5z(double rh, double dh, double date1, double date2)
10422		{
10423	2	double t, ph[] = new double[3], r5h[][] = new double[3][3], s5h[] = new double[3], sh[] = new double[3], vst[] = new double[3],
10424	2	rst[][] = new double[3][3], r5ht[][] = new double[3][3], pv5e[][] = new double[2][3], vv[] = new double[3];
10425
10426
10427		/* Time interval from fundamental epoch J2000.0 to given date (JY). */
10428	2	t = ((date1 - DJ00) + date2) / DJY;
10429
10430		/* Hipparcos barycentric position vector (normalized). */
10431	2	ph = jauS2c(rh,dh);
10432
10433		/* FK5 to Hipparcos orientation matrix and spin vector. */
10434	2	jauFk5hip(r5h, s5h);
10435
10436		/* Rotate the spin into the Hipparcos system. */
10437	2	sh = jauRxp(r5h, s5h);
10438
10439		/* Accumulated Hipparcos wrt FK5 spin over that interval. */
10440	2	vst = jauSxp(t,s5h);
10441
10442		/* Express the accumulated spin as a rotation matrix. */
10443	2	rst = jauRv2m(vst);
10444
10445		/* Rotation matrix: accumulated spin, then FK5 to Hipparcos. */
10446	2	r5ht = jauRxr(r5h, rst);
10447
10448		/* De-orient & de-spin the Hipparcos position into FK5 J2000.0. */
10449	2	pv5e[0] = jauTrxp(r5ht, ph);
10450
10451		/* Apply spin to the position giving a space motion. */
10452	2	vv = jauPxp(sh,ph);
10453
10454		/* De-orient & de-spin the Hipparcos space motion into FK5 J2000.0. */
10455	2	pv5e[1] = jauTrxp(r5ht, vv);
10456
10457		/* FK5 position/velocity pv-vector to spherical. */
10458	2	SphericalPositionVelocity pvs = jauPv2s(pv5e);
10459	2	double r5 = jauAnp(pvs.pos.theta);
10460
10461	2	return new CatalogCoords(r5, pvs.pos.phi, pvs.vel.theta, pvs.vel.phi, 0.0, 0.0);
10462
10463		}
10464
10465
10466		/**
10467		* Initialize an r-matrix to the identity matrix.
10468		*
10469		*<p>This function is derived from the International Astronomical Union's
10470		* SOFA (Standards Of Fundamental Astronomy) software collection.
10471		*
10472		*<p>Status: vector/matrix support function.
10473		*
10474		*<!-- Returned: -->
10475		* @param r double[3][3] <u>returned</u> r-matrix
10476		*
10477		*<p>Called:<ul>
10478		* <li>{@link #jauZr} zero r-matrix
10479		* </ul>
10480		*@version 2008 May 11
10481		*
10482		* @since Release 20101201
10483		*
10484		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10485		*/
10486		public static void jauIr(double r[][])
10487		{
10488	1302	jauZr(r);
10489	1302	r[0][0] = 1.0;
10490	1302	r[1][1] = 1.0;
10491	1302	r[2][2] = 1.0;
10492
10493	1302	return;
10494
10495		}
10496
10497
10498		/**
10499		* Julian Date to Gregorian year, month, day, and fraction of a day.
10500		*
10501		*<p>This function is derived from the International Astronomical Union's
10502		* SOFA (Standards Of Fundamental Astronomy) software collection.
10503		*
10504		*<p>Status: support function.
10505		*
10506		*<!-- Given: -->
10507		* @param dj1 double Julian Date (Notes 1, 2)
10508		* @param dj2 double Julian Date (Notes 1, 2)
10509		*
10510		* Returned (arguments):
10511		* iy int year
10512		* im int month
10513		* id int day
10514		* fd double fraction of day
10515		*
10516		* <!-- Returned (function value): -->
10517		* @return int status:
10518		* 0 = OK
10519		* -1 = unacceptable date (Note 3)
10520		*
10521		* <p>Notes:
10522		* <ol>
10523		*
10524		* <li> The earliest valid date is -68569.5 (-4900 March 1). The
10525		* largest value accepted is 10^9.
10526		*
10527		* <li> The Julian Date is apportioned in any convenient way between
10528		* the arguments dj1 and dj2. For example, JD=2450123.7 could
10529		* be expressed in any of these ways, among others:
10530		*<pre>
10531		* dj1 dj2
10532		*
10533		* 2450123.7 0.0 (JD method)
10534		* 2451545.0 -1421.3 (J2000 method)
10535		* 2400000.5 50123.2 (MJD method)
10536		* 2450123.5 0.2 (date & time method)
10537		*</pre>
10538		* <li> In early eras the conversion is from the "proleptic Gregorian
10539		* calendar"; no account is taken of the date(s) of adoption of
10540		* the Gregorian calendar, nor is the AD/BC numbering convention
10541		* observed.
10542		*</ol>
10543		*<p>Reference:
10544		*
10545		* <p>Explanatory Supplement to the Astronomical Almanac,
10546		* P. Kenneth Seidelmann (ed), University Science Books (1992),
10547		* Section 12.92 (p604).
10548		*
10549		*@version 2008 May 26
10550		*
10551		* @since Release 20101201
10552		*
10553		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10554		*/
10555		public static Calendar jauJd2cal(double dj1, double dj2) throws JSOFAIllegalParameter
10556		{
10557		/* Minimum and maximum allowed JD */
10558	162	final double djmin = -68569.5;
10559	162	final double djmax = 1e9;
10560
10561		long jd, l, n, i, k;
10562		double dj, d1, d2, f1, f2, f, d;
10563
10564
10565		/* Verify date is acceptable. */
10566	162	dj = dj1 + dj2;
10567	162	if (dj < djmin \|\| dj > djmax) throw new JSOFAIllegalParameter("input julian date out of range", -1);
10568
10569		/* Copy the date, big then small, and re-align to midnight. */
10570	162	if (dj1 >= dj2) {
10571	162	d1 = dj1;
10572	162	d2 = dj2;
10573		} else {
10574	0	d1 = dj2;
10575	0	d2 = dj1;
10576		}
10577	162	d2 -= 0.5;
10578
10579		/* Separate day and fraction. */
10580	162	f1 = fmod(d1, 1.0);
10581	162	f2 = fmod(d2, 1.0);
10582	162	f = fmod(f1 + f2, 1.0);
10583	162	if (f < 0.0) f += 1.0;
10584	162	d = floor(d1 - f1) + floor(d2 - f2) + floor(f1 + f2 - f);
10585	162	jd = (long) floor(d) + 1L;
10586
10587		/* Express day in Gregorian calendar. */
10588	162	l = jd + 68569L;
10589	162	n = (4L * l) / 146097L;
10590	162	l -= (146097L * n + 3L) / 4L;
10591	162	i = (4000L * (l + 1L)) / 1461001L;
10592	162	l -= (1461L * i) / 4L - 31L;
10593	162	k = (80L * l) / 2447L;
10594	162	int id = (int) (l - (2447L * k) / 80L);
10595	162	l = k / 11L;
10596	162	int im = (int) (k + 2L - 12L * l);
10597	162	int iy = (int) (100L * (n - 49L) + i + l);
10598
10599
10600	162	return new Calendar(iy, im, id, f);
10601
10602		}
10603
10604		/**
10605		* Julian Date to Gregorian Calendar, expressed in a form convenient
10606		* for formatting messages: rounded to a specified precision.
10607		*
10608		*<p>This function is derived from the International Astronomical Union's
10609		* SOFA (Standards Of Fundamental Astronomy) software collection.
10610		*
10611		*<p>Status: support function.
10612		*
10613		*<!-- Given: -->
10614		* @param ndp int number of decimal places of days in fraction
10615		* @param dj1 double dj1+dj2 = Julian Date (Note 1)
10616		* @param dj2 double dj1+dj2 = Julian Date (Note 1)
10617		*
10618		*<!-- Returned: -->
10619		* @param iymdf int[4] <u>returned</u> year, month, day, fraction in Gregorian calendar
10620		*
10621		*
10622		* <!-- Returned (function value): -->
10623		* @return int status:
10624		* -1 = date out of range
10625		* 0 = OK
10626		* +1 = NDP not 0-9 (interpreted as 0)
10627		*
10628		* <p>Notes:
10629		* <ol>
10630		*
10631		* <li> The Julian Date is apportioned in any convenient way between
10632		* the arguments dj1 and dj2. For example, JD=2450123.7 could
10633		* be expressed in any of these ways, among others:
10634		*<pre>
10635		* dj1 dj2
10636		*
10637		* 2450123.7 0.0 (JD method)
10638		* 2451545.0 -1421.3 (J2000 method)
10639		* 2400000.5 50123.2 (MJD method)
10640		* 2450123.5 0.2 (date & time method)
10641		*</pre>
10642		* <li> In early eras the conversion is from the "Proleptic Gregorian
10643		* Calendar"; no account is taken of the date(s) of adoption of
10644		* the Gregorian Calendar, nor is the AD/BC numbering convention
10645		* observed.
10646		*
10647		* <li> Refer to the function jauJd2cal.
10648		*
10649		* <li> NDP should be 4 or less if internal overflows are to be
10650		* avoided on machines which use 16-bit integers.
10651		*</ol>
10652		*<p>Called:<ul>
10653		* <li>{@link #jauJd2cal} JD to Gregorian calendar
10654		* </ul>
10655		*<p>Reference:
10656		*
10657		* <p>Explanatory Supplement to the Astronomical Almanac,
10658		* P. Kenneth Seidelmann (ed), University Science Books (1992),
10659		* Section 12.92 (p604).
10660		*
10661		*@version 2008 October 28
10662		*
10663		* @since Release 20101201
10664		*
10665		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10666		*/
10667		public static int jauJdcalf(int ndp, double dj1, double dj2, int iymdf[])
10668		{
10669		int j;
10670		double denom, d1, d2, f1, f2, f;
10671
10672
10673		/* Denominator of fraction (e.g. 100 for 2 decimal places). */
10674	2	if ((ndp >= 0) && (ndp <= 9)) {
10675	2	j = 0;
10676	2	denom = pow(10.0, ndp);
10677		} else {
10678	0	j = 1;
10679	0	denom = 1.0;
10680		}
10681
10682		/* Copy the date, big then small, and realign to midnight. */
10683	2	if (dj1 >= dj2) {
10684	2	d1 = dj1;
10685	2	d2 = dj2;
10686		} else {
10687	0	d1 = dj2;
10688	0	d2 = dj1;
10689		}
10690	2	d2 -= 0.5;
10691
10692		/* Separate days and fractions. */
10693	2	f1 = fmod(d1, 1.0);
10694	2	f2 = fmod(d2, 1.0);
10695	2	d1 = floor(d1 - f1);
10696	2	d2 = floor(d2 - f2);
10697
10698		/* Round the total fraction to the specified number of places. */
10699	2	f = floor((f1 + f2) * denom) / denom;
10700
10701		/* Re-assemble the rounded date and re-align to noon. */
10702	2	d2 += f + 0.5;
10703
10704		/* Convert to Gregorian Calendar. */
10705		try {
10706	2	Calendar cal = jauJd2cal(d1, d2);
10707	2	iymdf[0] = cal.iy;
10708	2	iymdf[1] = cal.im;
10709	2	iymdf[2] = cal.id;
10710	2	iymdf[3] = (int) (cal.fd * denom);
10711	0	} catch (JSOFAIllegalParameter e) {
10712	0	j = -1;
10713	2	}
10714
10715		/* Return the status. */
10716	2	return j;
10717
10718		}
10719
10720
10721		/**
10722		* Form the matrix of nutation for a given date, IAU 2000A model.
10723		*
10724		*<p>This function is derived from the International Astronomical Union's
10725		* SOFA (Standards Of Fundamental Astronomy) software collection.
10726		*
10727		*<p>Status: support function.
10728		*
10729		*<!-- Given: -->
10730		* @param date1 double TT as a 2-part Julian Date (Note 1)
10731		* @param date2 double TT as a 2-part Julian Date (Note 1)
10732		*
10733		*<!-- Returned: -->
10734		* @return rmatn double[3][3] <u>returned</u> nutation matrix
10735		*
10736		* <p>Notes:
10737		* <ol>
10738		*
10739		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
10740		* convenient way between the two arguments. For example,
10741		* JD(TT)=2450123.7 could be expressed in any of these ways,
10742		* among others:
10743		*<pre>
10744		* date1 date2
10745		*
10746		* 2450123.7 0.0 (JD method)
10747		* 2451545.0 -1421.3 (J2000 method)
10748		* 2400000.5 50123.2 (MJD method)
10749		* 2450123.5 0.2 (date & time method)
10750		*</pre>
10751		* The JD method is the most natural and convenient to use in
10752		* cases where the loss of several decimal digits of resolution
10753		* is acceptable. The J2000 method is best matched to the way
10754		* the argument is handled internally and will deliver the
10755		* optimum resolution. The MJD method and the date & time methods
10756		* are both good compromises between resolution and convenience.
10757		*
10758		* <li> The matrix operates in the sense V(true) = rmatn * V(mean), where
10759		* the p-vector V(true) is with respect to the true equatorial triad
10760		* of date and the p-vector V(mean) is with respect to the mean
10761		* equatorial triad of date.
10762		*
10763		* <li> A faster, but slightly less accurate result (about 1 mas), can be
10764		* obtained by using instead the jauNum00b function.
10765		*</ol>
10766		*<p>Called:<ul>
10767		* <li>{@link #jauPn00a} bias/precession/nutation, IAU 2000A
10768		* </ul>
10769		*<p>Reference:
10770		*
10771		* <p>Explanatory Supplement to the Astronomical Almanac,
10772		* P. Kenneth Seidelmann (ed), University Science Books (1992),
10773		* Section 3.222-3 (p114).
10774		*
10775		*@version 2008 May 12
10776		*
10777		* @since Release 20101201
10778		*
10779		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10780		*/
10781		public static double[][] jauNum00a(double date1, double date2)
10782		{
10783
10784		/* Obtain the required matrix (discarding other results). */
10785	2	PrecessionNutation pn = jauPn00a(date1, date2);
10786
10787	2	return pn.rn ;
10788
10789		}
10790
10791
10792		/**
10793		* Form the matrix of nutation for a given date, IAU 2000B model.
10794		*
10795		*<p>This function is derived from the International Astronomical Union's
10796		* SOFA (Standards Of Fundamental Astronomy) software collection.
10797		*
10798		*<p>Status: support function.
10799		*
10800		*<!-- Given: -->
10801		* @param date1 double TT as a 2-part Julian Date (Note 1)
10802		* @param date2 double TT as a 2-part Julian Date (Note 1)
10803		*
10804		*<!-- Returned: -->
10805		* @return rmatn double[3][3] <u>returned</u> nutation matrix
10806		*
10807		* <p>Notes:
10808		* <ol>
10809		*
10810		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
10811		* convenient way between the two arguments. For example,
10812		* JD(TT)=2450123.7 could be expressed in any of these ways,
10813		* among others:
10814		*<pre>
10815		* date1 date2
10816		*
10817		* 2450123.7 0.0 (JD method)
10818		* 2451545.0 -1421.3 (J2000 method)
10819		* 2400000.5 50123.2 (MJD method)
10820		* 2450123.5 0.2 (date & time method)
10821		*</pre>
10822		* The JD method is the most natural and convenient to use in
10823		* cases where the loss of several decimal digits of resolution
10824		* is acceptable. The J2000 method is best matched to the way
10825		* the argument is handled internally and will deliver the
10826		* optimum resolution. The MJD method and the date & time methods
10827		* are both good compromises between resolution and convenience.
10828		*
10829		* <li> The matrix operates in the sense V(true) = rmatn * V(mean), where
10830		* the p-vector V(true) is with respect to the true equatorial triad
10831		* of date and the p-vector V(mean) is with respect to the mean
10832		* equatorial triad of date.
10833		*
10834		* <li> The present function is faster, but slightly less accurate (about
10835		* 1 mas), than the jauNum00a function.
10836		*</ol>
10837		*<p>Called:<ul>
10838		* <li>{@link #jauPn00b} bias/precession/nutation, IAU 2000B
10839		* </ul>
10840		*<p>Reference:
10841		*
10842		* <p>Explanatory Supplement to the Astronomical Almanac,
10843		* P. Kenneth Seidelmann (ed), University Science Books (1992),
10844		* Section 3.222-3 (p114).
10845		*
10846		*@version 2008 May 12
10847		*
10848		* @since Release 20101201
10849		*
10850		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10851		*/
10852		public static double[][] jauNum00b(double date1, double date2)
10853		{
10854
10855		/* Obtain the required matrix (discarding other results). */
10856	2	PrecessionNutation pn = jauPn00b(date1, date2);
10857
10858	2	return pn.rn;
10859
10860		}
10861
10862
10863		/**
10864		* Form the matrix of nutation for a given date, IAU 2006/2000A model.
10865		*
10866		*<p>This function is derived from the International Astronomical Union's
10867		* SOFA (Standards Of Fundamental Astronomy) software collection.
10868		*
10869		*<p>Status: support function.
10870		*
10871		*<!-- Given: -->
10872		* @param date1 double TT as a 2-part Julian Date (Note 1)
10873		* @param date2 double TT as a 2-part Julian Date (Note 1)
10874		*
10875		*<!-- Returned: -->
10876		* @return rmatn double[3][3] <u>returned</u> nutation matrix
10877		*
10878		* <p>Notes:
10879		* <ol>
10880		*
10881		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
10882		* convenient way between the two arguments. For example,
10883		* JD(TT)=2450123.7 could be expressed in any of these ways,
10884		* among others:
10885		*<pre>
10886		* date1 date2
10887		*
10888		* 2450123.7 0.0 (JD method)
10889		* 2451545.0 -1421.3 (J2000 method)
10890		* 2400000.5 50123.2 (MJD method)
10891		* 2450123.5 0.2 (date & time method)
10892		*</pre>
10893		* The JD method is the most natural and convenient to use in
10894		* cases where the loss of several decimal digits of resolution
10895		* is acceptable. The J2000 method is best matched to the way
10896		* the argument is handled internally and will deliver the
10897		* optimum resolution. The MJD method and the date & time methods
10898		* are both good compromises between resolution and convenience.
10899		*
10900		* <li> The matrix operates in the sense V(true) = rmatn * V(mean), where
10901		* the p-vector V(true) is with respect to the true equatorial triad
10902		* of date and the p-vector V(mean) is with respect to the mean
10903		* equatorial triad of date.
10904		*</ol>
10905		*<p>Called:<ul>
10906		* <li>{@link #jauObl06} mean obliquity, IAU 2006
10907		* <li>{@link #jauNut06a} nutation, IAU 2006/2000A
10908		* <li>{@link #jauNumat} form nutation matrix
10909		* </ul>
10910		*<p>Reference:
10911		*
10912		* <p>Explanatory Supplement to the Astronomical Almanac,
10913		* P. Kenneth Seidelmann (ed), University Science Books (1992),
10914		* Section 3.222-3 (p114).
10915		*
10916		*@version 2008 May 12
10917		*
10918		* @since Release 20101201
10919		*
10920		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10921		*/
10922		public static double[][] jauNum06a(double date1, double date2)
10923		{
10924		double eps, rmatn[][];
10925
10926
10927		/* Mean obliquity. */
10928	2	eps = jauObl06(date1, date2);
10929
10930		/* Nutation components. */
10931	2	NutationTerms nut = jauNut06a(date1, date2);
10932
10933		/* Nutation matrix. */
10934	2	rmatn = jauNumat(eps, nut.dpsi, nut.deps);
10935
10936	2	return rmatn;
10937
10938		}
10939
10940
10941		/**
10942		* Form the matrix of nutation.
10943		*
10944		*<p>This function is derived from the International Astronomical Union's
10945		* SOFA (Standards Of Fundamental Astronomy) software collection.
10946		*
10947		*<p>Status: support function.
10948		*
10949		*<!-- Given: -->
10950		* @param epsa double mean obliquity of date (Note 1)
10951		* @param dpsi double nutation (Note 2)
10952		* @param deps double nutation (Note 2)
10953		*
10954		*<!-- Returned: -->
10955		* @return rmatn double[3][3] <u>returned</u> nutation matrix (Note 3)
10956		*
10957		* <p>Notes:
10958		* <ol>
10959		*
10960		*
10961		* <li> The supplied mean obliquity epsa, must be consistent with the
10962		* precession-nutation models from which dpsi and deps were obtained.
10963		*
10964		* <li> The caller is responsible for providing the nutation components;
10965		* they are in longitude and obliquity, in radians and are with
10966		* respect to the equinox and ecliptic of date.
10967		*
10968		* <li> The matrix operates in the sense V(true) = rmatn * V(mean),
10969		* where the p-vector V(true) is with respect to the true
10970		* equatorial triad of date and the p-vector V(mean) is with
10971		* respect to the mean equatorial triad of date.
10972		*</ol>
10973		*<p>Called:<ul>
10974		* <li>{@link #jauIr} initialize r-matrix to identity
10975		* <li>{@link #jauRx} rotate around X-axis
10976		* <li>{@link #jauRz} rotate around Z-axis
10977		* </ul>
10978		*<p>Reference:
10979		*
10980		* <p>Explanatory Supplement to the Astronomical Almanac,
10981		* P. Kenneth Seidelmann (ed), University Science Books (1992),
10982		* Section 3.222-3 (p114).
10983		*
10984		*@version 2008 May 11
10985		*
10986		* @since Release 20101201
10987		*
10988		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
10989		*/
10990		public static double[][] jauNumat(double epsa, double dpsi, double deps)
10991		{
10992	40	double rmatn[][] = new double[3][3];
10993		/* Build the rotation matrix. */
10994	40	jauIr(rmatn);
10995	40	jauRx(epsa, rmatn);
10996	40	jauRz(-dpsi, rmatn);
10997	40	jauRx(-(epsa + deps), rmatn);
10998
10999	40	return rmatn;
11000
11001		}
11002		/**
11003		* Nutation Terms.
11004		* .
11005		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 21 Nov 2011
11006		* @version $Revision$ $date$
11007		*/
11008		public static class NutationTerms {
11009		/** nutation component in longitude */
11010		public double dpsi;
11011		/** nutation component in obliquity */
11012		public double deps;
11013	182	public NutationTerms(double dpsi, double deps) {
11014	182	this.dpsi = dpsi;
11015	182	this.deps = deps;
11016	182	}
11017		}
11018		/**
11019		* Nutation, IAU 2000A model (MHB2000 luni-solar and planetary nutation
11020		* with free core nutation omitted).
11021		*
11022		*<p>This function is derived from the International Astronomical Union's
11023		* SOFA (Standards Of Fundamental Astronomy) software collection.
11024		*
11025		*<p>Status: canonical model.
11026		*
11027		*<!-- Given: -->
11028		* @param date1 double TT as a 2-part Julian Date (Note 1)
11029		* @param date2 double TT as a 2-part Julian Date (Note 1)
11030		*
11031		*<!-- Returned: -->
11032		* @return <u>returned</u> nutation, luni-solar + planetary (Note 2)
11033		*
11034		* <p>Notes:
11035		* <ol>
11036		*
11037		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
11038		* convenient way between the two arguments. For example,
11039		* JD(TT)=2450123.7 could be expressed in any of these ways,
11040		* among others:
11041		*<pre>
11042		* date1 date2
11043		*
11044		* 2450123.7 0.0 (JD method)
11045		* 2451545.0 -1421.3 (J2000 method)
11046		* 2400000.5 50123.2 (MJD method)
11047		* 2450123.5 0.2 (date & time method)
11048		*</pre>
11049		* The JD method is the most natural and convenient to use in
11050		* cases where the loss of several decimal digits of resolution
11051		* is acceptable. The J2000 method is best matched to the way
11052		* the argument is handled internally and will deliver the
11053		* optimum resolution. The MJD method and the date & time methods
11054		* are both good compromises between resolution and convenience.
11055		*
11056		* <li> The nutation components in longitude and obliquity are in radians
11057		* and with respect to the equinox and ecliptic of date. The
11058		* obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
11059		* value of 84381.448 arcsec.
11060		*
11061		* Both the luni-solar and planetary nutations are included. The
11062		* latter are due to direct planetary nutations and the
11063		* perturbations of the lunar and terrestrial orbits.
11064		*
11065		* <li> The function computes the MHB2000 nutation series with the
11066		* associated corrections for planetary nutations. It is an
11067		* implementation of the nutation part of the IAU 2000A precession-
11068		* nutation model, formally adopted by the IAU General Assembly in
11069		* 2000, namely MHB2000 (Mathews et al. 2002), but with the free
11070		* core nutation (FCN - see Note 4) omitted.
11071		*
11072		* <li> The full MHB2000 model also contains contributions to the
11073		* nutations in longitude and obliquity due to the free-excitation
11074		* of the free-core-nutation during the period 1979-2000. These FCN
11075		* terms, which are time-dependent and unpredictable, are NOT
11076		* included in the present function and, if required, must be
11077		* independently computed. With the FCN corrections included, the
11078		* present function delivers a pole which is at current epochs
11079		* accurate to a few hundred microarcseconds. The omission of FCN
11080		* introduces further errors of about that size.
11081		*
11082		* <li> The present function provides classical nutation. The MHB2000
11083		* algorithm, from which it is adapted, deals also with (i) the
11084		* offsets between the GCRS and mean poles and (ii) the adjustments
11085		* in longitude and obliquity due to the changed precession rates.
11086		* These additional functions, namely frame bias and precession
11087		* adjustments, are supported by the JSOFA functions jauBi00 and
11088		* jauPr00.
11089		*
11090		* <li> The MHB2000 algorithm also provides "total" nutations, comprising
11091		* the arithmetic sum of the frame bias, precession adjustments,
11092		* luni-solar nutation and planetary nutation. These total
11093		* nutations can be used in combination with an existing IAU 1976
11094		* precession implementation, such as jauPmat76, to deliver GCRS-
11095		* to-true predictions of sub-mas accuracy at current dates.
11096		* However, there are three shortcomings in the MHB2000 model that
11097		* must be taken into account if more accurate or definitive results
11098		* are required (see Wallace 2002):
11099		*
11100		* (i) The MHB2000 total nutations are simply arithmetic sums,
11101		* yet in reality the various components are successive Euler
11102		* rotations. This slight lack of rigor leads to cross terms
11103		* that exceed 1 mas after a century. The rigorous procedure
11104		* is to form the GCRS-to-true rotation matrix by applying the
11105		* bias, precession and nutation in that order.
11106		*
11107		* (ii) Although the precession adjustments are stated to be with
11108		* respect to Lieske et al. (1977), the MHB2000 model does
11109		* not specify which set of Euler angles are to be used and
11110		* how the adjustments are to be applied. The most literal
11111		* and straightforward procedure is to adopt the 4-rotation
11112		* epsilon_0, psi_A, omega_A, xi_A option, and to add DPSIPR
11113		* to psi_A and DEPSPR to both omega_A and eps_A.
11114		*
11115		* (iii) The MHB2000 model predates the determination by Chapront
11116		* et al. (2002) of a 14.6 mas displacement between the
11117		* J2000.0 mean equinox and the origin of the ICRS frame. It
11118		* should, however, be noted that neglecting this displacement
11119		* when calculating star coordinates does not lead to a
11120		* 14.6 mas change in right ascension, only a small second-
11121		* order distortion in the pattern of the precession-nutation
11122		* effect.
11123		*
11124		* For these reasons, the JSOFA functions do not generate the "total
11125		* nutations" directly, though they can of course easily be
11126		* generated by calling jauBi00, jauPr00 and the present function
11127		* and adding the results.
11128		*
11129		* <li> The MHB2000 model contains 41 instances where the same frequency
11130		* appears multiple times, of which 38 are duplicates and three are
11131		* triplicates. To keep the present code close to the original MHB
11132		* algorithm, this small inefficiency has not been corrected.
11133		*</ol>
11134		*<p>Called:<ul>
11135		* <li>{@link #jauFal03} mean anomaly of the Moon
11136		* <li>{@link #jauFaf03} mean argument of the latitude of the Moon
11137		* <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
11138		* <li>{@link #jauFame03} mean longitude of Mercury
11139		* <li>{@link #jauFave03} mean longitude of Venus
11140		* <li>{@link #jauFae03} mean longitude of Earth
11141		* <li>{@link #jauFama03} mean longitude of Mars
11142		* <li>{@link #jauFaju03} mean longitude of Jupiter
11143		* <li>{@link #jauFasa03} mean longitude of Saturn
11144		* <li>{@link #jauFaur03} mean longitude of Uranus
11145		* <li>{@link #jauFapa03} general accumulated precession in longitude
11146		* </ul>
11147		*<p>References:
11148		*
11149		* <p>Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
11150		* Astron.Astrophys. 387, 700
11151		*
11152		* <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
11153		* Astron.Astrophys. 58, 1-16
11154		*
11155		* <p>Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
11156		* 107, B4. The MHB_2000 code itself was obtained on 9th September
11157		* 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
11158		*
11159		* <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
11160		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
11161		*
11162		* <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
11163		* Astron.Astrophys.Supp.Ser. 135, 111
11164		*
11165		* <p>Wallace, P.T., "Software for Implementing the IAU 2000
11166		* Resolutions", in IERS Workshop 5.1 (2002)
11167		*
11168		*@version 2009 December 17
11169		*
11170		* @since Release 20101201
11171		*
11172		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
11173		*/
11174		public static NutationTerms jauNut00a(double date1, double date2 )
11175		{
11176		int i;
11177		double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
11178		al, af, ad, aom, alme, alve, alea, alma,
11179		alju, alsa, alur, alne, apa, dpsils, depsls,
11180		dpsipl, depspl;
11181
11182		/* Units of 0.1 microarcsecond to radians */
11183	68	final double U2R = DAS2R / 1e7;
11184
11185		/* ------------------------- */
11186		/* Luni-Solar nutation model */
11187		/* ------------------------- */
11188
11189		/* The units for the sine and cosine coefficients are */
11190		/* 0.1 microarcsecond and the same per Julian century */
11191
11192		final class NutationModel {
11193		int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
11194		double sp,spt,cp; /* longitude sin, tsin, cos coefficients /
11195		double ce,cet,se; /* obliquity cos, tcos, sin coefficients /
11196		public NutationModel(int nl,int nlp,int nf,int nd, int nom,
11197		double sp,double spt,double cp,
11198	46104	double ce,double cet,double se ) {
11199	46104	this.nl = nl;
11200	46104	this.nlp = nlp;
11201	46104	this.nf = nf;
11202	46104	this.nd = nd;
11203	46104	this.nom = nom;
11204	46104	this.sp = sp;
11205	46104	this.spt = spt;
11206	46104	this.cp = cp;
11207	46104	this.ce = ce;
11208	46104	this.cet = cet;
11209	46104	this.se = se;
11210	46104	}
11211		}
11212
11213	68	NutationModel xls[] = {
11214
11215		/* 1- 10 */
11216		new NutationModel( 0, 0, 0, 0, 1,
11217		-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0),
11218		new NutationModel( 0, 0, 2,-2, 2,
11219		-13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0),
11220		new NutationModel( 0, 0, 2, 0, 2,-2276413.0,-234.0,2796.0,978459.0,-485.0, 1374.0),
11221		new NutationModel( 0, 0, 0, 0, 2,2074554.0, 207.0, -698.0,-897492.0,470.0, -291.0),
11222		new NutationModel( 0, 1, 0, 0, 0,1475877.0,-3633.0,11817.0,73871.0,-184.0,-1924.0),
11223		new NutationModel( 0, 1, 2,-2, 2,-516821.0,1226.0, -524.0,224386.0,-677.0, -174.0),
11224		new NutationModel( 1, 0, 0, 0, 0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0),
11225		new NutationModel( 0, 0, 2, 0, 1,-387298.0,-367.0, 380.0, 200728.0, 18.0, 318.0),
11226		new NutationModel( 1, 0, 2, 0, 2,-301461.0, -36.0, 816.0, 129025.0,-63.0, 367.0),
11227		new NutationModel( 0,-1, 2,-2, 2, 215829.0,-494.0, 111.0, -95929.0,299.0, 132.0),
11228
11229		/* 11-20 */
11230		new NutationModel( 0, 0, 2,-2, 1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0),
11231		new NutationModel(-1, 0, 2, 0, 2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0),
11232		new NutationModel(-1, 0, 0, 2, 0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0),
11233		new NutationModel( 1, 0, 0, 0, 1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0),
11234		new NutationModel(-1, 0, 0, 0, 1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0),
11235		new NutationModel(-1, 0, 2, 2, 2, -59641.0, -11.0, 149.0, 25543.0,-11.0, 66.0),
11236		new NutationModel( 1, 0, 2, 0, 1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0),
11237		new NutationModel(-2, 0, 2, 0, 1, 45893.0, 50.0, 31.0, -24236.0,-10.0, 20.0),
11238		new NutationModel( 0, 0, 0, 2, 0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0),
11239		new NutationModel( 0, 0, 2, 2, 2, -38571.0, -1.0, 158.0, 16452.0,-11.0, 68.0),
11240
11241		/* 21-30 */
11242		new NutationModel( 0,-2, 2,-2, 2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0),
11243		new NutationModel(-2, 0, 0, 2, 0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0),
11244		new NutationModel( 2, 0, 2, 0, 2, -31046.0, -1.0, 131.0, 13238.0,-11.0, 59.0),
11245		new NutationModel( 1, 0, 2,-2, 2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0),
11246		new NutationModel(-1, 0, 2, 0, 1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0),
11247		new NutationModel( 2, 0, 0, 0, 0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0),
11248		new NutationModel( 0, 0, 2, 0, 0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0),
11249		new NutationModel( 0, 1, 0, 0, 1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0),
11250		new NutationModel(-1, 0, 0, 2, 1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0),
11251		new NutationModel( 0, 2, 2,-2, 2, -15794.0, 72.0, -16.0, 6850.0,-42.0, -5.0),
11252
11253		/* 31-40 */
11254		new NutationModel( 0, 0,-2, 2, 0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0),
11255		new NutationModel( 1, 0, 0,-2, 1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0),
11256		new NutationModel( 0,-1, 0, 0, 1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0),
11257		new NutationModel(-1, 0, 2, 2, 1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0),
11258		new NutationModel( 0, 2, 0, 0, 0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0),
11259		new NutationModel( 1, 0, 2, 2, 2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0),
11260		new NutationModel(-2, 0, 2, 0, 0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0),
11261		new NutationModel( 0, 1, 2, 0, 2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0),
11262		new NutationModel( 0, 0, 2, 2, 1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0),
11263		new NutationModel( 0,-1, 2, 0, 2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0),
11264
11265		/* 41-50 */
11266		new NutationModel( 0, 0, 0, 2, 1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0),
11267		new NutationModel( 1, 0, 2,-2, 1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0),
11268		new NutationModel( 2, 0, 2,-2, 2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0),
11269		new NutationModel(-2, 0, 0, 2, 1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0),
11270		new NutationModel( 2, 0, 2, 0, 1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0),
11271		new NutationModel( 0,-1, 2,-2, 1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0),
11272		new NutationModel( 0, 0, 0,-2, 1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0),
11273		new NutationModel(-1,-1, 0, 2, 0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0),
11274		new NutationModel( 2, 0, 0,-2, 1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0),
11275		new NutationModel( 1, 0, 0, 2, 0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0),
11276
11277		/* 51-60 */
11278		new NutationModel( 0, 1, 2,-2, 1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0),
11279		new NutationModel( 1,-1, 0, 0, 0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0),
11280		new NutationModel(-2, 0, 2, 0, 2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0),
11281		new NutationModel( 3, 0, 2, 0, 2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0),
11282		new NutationModel( 0,-1, 0, 2, 0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0),
11283		new NutationModel( 1,-1, 2, 0, 2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0),
11284		new NutationModel( 0, 0, 0, 1, 0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0),
11285		new NutationModel(-1,-1, 2, 2, 2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0),
11286		new NutationModel(-1, 0, 2, 0, 0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0),
11287		new NutationModel( 0,-1, 2, 2, 2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0),
11288
11289		/* 61-70 */
11290		new NutationModel(-2, 0, 0, 0, 1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0),
11291		new NutationModel( 1, 1, 2, 0, 2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0),
11292		new NutationModel( 2, 0, 0, 0, 1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0),
11293		new NutationModel(-1, 1, 0, 1, 0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0),
11294		new NutationModel( 1, 1, 0, 0, 0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0),
11295		new NutationModel( 1, 0, 2, 0, 0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0),
11296		new NutationModel(-1, 0, 2,-2, 1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0),
11297		new NutationModel( 1, 0, 0, 0, 2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0),
11298		new NutationModel(-1, 0, 0, 1, 0, 4026.0, 0.0, -353.0, -553.0, 0.0, -139.0),
11299		new NutationModel( 0, 0, 2, 1, 2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0),
11300
11301		/* 71-80 */
11302		new NutationModel(-1, 0, 2, 4, 2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0),
11303		new NutationModel(-1, 1, 0, 1, 1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0),
11304		new NutationModel( 0,-2, 2,-2, 1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0),
11305		new NutationModel( 1, 0, 2, 2, 1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0),
11306		new NutationModel(-2, 0, 2, 2, 2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0),
11307		new NutationModel(-1, 0, 0, 0, 2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0),
11308		new NutationModel( 1, 1, 2,-2, 2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0),
11309		new NutationModel(-2, 0, 2, 4, 2, -1214.0, 0.0, 5.0, 518.0, 0.0, 2.0),
11310		new NutationModel(-1, 0, 4, 0, 2, 1146.0, 0.0, -3.0, -490.0, 0.0, -1.0),
11311		new NutationModel( 2, 0, 2,-2, 1, 1019.0, 0.0, -1.0, -527.0, 0.0, -1.0),
11312
11313		/* 81-90 */
11314		new NutationModel( 2, 0, 2, 2, 2, -1100.0, 0.0, 9.0, 465.0, 0.0, 4.0),
11315		new NutationModel( 1, 0, 0, 2, 1, -970.0, 0.0, 2.0, 496.0, 0.0, 1.0),
11316		new NutationModel( 3, 0, 0, 0, 0, 1575.0, 0.0, -6.0, -50.0, 0.0, 0.0),
11317		new NutationModel( 3, 0, 2,-2, 2, 934.0, 0.0, -3.0, -399.0, 0.0, -1.0),
11318		new NutationModel( 0, 0, 4,-2, 2, 922.0, 0.0, -1.0, -395.0, 0.0, -1.0),
11319		new NutationModel( 0, 1, 2, 0, 1, 815.0, 0.0, -1.0, -422.0, 0.0, -1.0),
11320		new NutationModel( 0, 0,-2, 2, 1, 834.0, 0.0, 2.0, -440.0, 0.0, 1.0),
11321		new NutationModel( 0, 0, 2,-2, 3, 1248.0, 0.0, 0.0, -170.0, 0.0, 1.0),
11322		new NutationModel(-1, 0, 0, 4, 0, 1338.0, 0.0, -5.0, -39.0, 0.0, 0.0),
11323		new NutationModel( 2, 0,-2, 0, 1, 716.0, 0.0, -2.0, -389.0, 0.0, -1.0),
11324
11325		/* 91-100 */
11326		new NutationModel(-2, 0, 0, 4, 0, 1282.0, 0.0, -3.0, -23.0, 0.0, 1.0),
11327		new NutationModel(-1,-1, 0, 2, 1, 742.0, 0.0, 1.0, -391.0, 0.0, 0.0),
11328		new NutationModel(-1, 0, 0, 1, 1, 1020.0, 0.0, -25.0, -495.0, 0.0, -10.0),
11329		new NutationModel( 0, 1, 0, 0, 2, 715.0, 0.0, -4.0, -326.0, 0.0, 2.0),
11330		new NutationModel( 0, 0,-2, 0, 1, -666.0, 0.0, -3.0, 369.0, 0.0, -1.0),
11331		new NutationModel( 0,-1, 2, 0, 1, -667.0, 0.0, 1.0, 346.0, 0.0, 1.0),
11332		new NutationModel( 0, 0, 2,-1, 2, -704.0, 0.0, 0.0, 304.0, 0.0, 0.0),
11333		new NutationModel( 0, 0, 2, 4, 2, -694.0, 0.0, 5.0, 294.0, 0.0, 2.0),
11334		new NutationModel(-2,-1, 0, 2, 0, -1014.0, 0.0, -1.0, 4.0, 0.0, -1.0),
11335		new NutationModel( 1, 1, 0,-2, 1, -585.0, 0.0, -2.0, 316.0, 0.0, -1.0),
11336
11337		/* 101-110 */
11338		new NutationModel(-1, 1, 0, 2, 0, -949.0, 0.0, 1.0, 8.0, 0.0, -1.0),
11339		new NutationModel(-1, 1, 0, 1, 2, -595.0, 0.0, 0.0, 258.0, 0.0, 0.0),
11340		new NutationModel( 1,-1, 0, 0, 1, 528.0, 0.0, 0.0, -279.0, 0.0, 0.0),
11341		new NutationModel( 1,-1, 2, 2, 2, -590.0, 0.0, 4.0, 252.0, 0.0, 2.0),
11342		new NutationModel(-1, 1, 2, 2, 2, 570.0, 0.0, -2.0, -244.0, 0.0, -1.0),
11343		new NutationModel( 3, 0, 2, 0, 1, -502.0, 0.0, 3.0, 250.0, 0.0, 2.0),
11344		new NutationModel( 0, 1,-2, 2, 0, -875.0, 0.0, 1.0, 29.0, 0.0, 0.0),
11345		new NutationModel(-1, 0, 0,-2, 1, -492.0, 0.0, -3.0, 275.0, 0.0, -1.0),
11346		new NutationModel( 0, 1, 2, 2, 2, 535.0, 0.0, -2.0, -228.0, 0.0, -1.0),
11347		new NutationModel(-1,-1, 2, 2, 1, -467.0, 0.0, 1.0, 240.0, 0.0, 1.0),
11348
11349		/* 111-120 */
11350		new NutationModel( 0,-1, 0, 0, 2, 591.0, 0.0, 0.0, -253.0, 0.0, 0.0),
11351		new NutationModel( 1, 0, 2,-4, 1, -453.0, 0.0, -1.0, 244.0, 0.0, -1.0),
11352		new NutationModel(-1, 0,-2, 2, 0, 766.0, 0.0, 1.0, 9.0, 0.0, 0.0),
11353		new NutationModel( 0,-1, 2, 2, 1, -446.0, 0.0, 2.0, 225.0, 0.0, 1.0),
11354		new NutationModel( 2,-1, 2, 0, 2, -488.0, 0.0, 2.0, 207.0, 0.0, 1.0),
11355		new NutationModel( 0, 0, 0, 2, 2, -468.0, 0.0, 0.0, 201.0, 0.0, 0.0),
11356		new NutationModel( 1,-1, 2, 0, 1, -421.0, 0.0, 1.0, 216.0, 0.0, 1.0),
11357		new NutationModel(-1, 1, 2, 0, 2, 463.0, 0.0, 0.0, -200.0, 0.0, 0.0),
11358		new NutationModel( 0, 1, 0, 2, 0, -673.0, 0.0, 2.0, 14.0, 0.0, 0.0),
11359		new NutationModel( 0,-1,-2, 2, 0, 658.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11360
11361		/* 121-130 */
11362		new NutationModel( 0, 3, 2,-2, 2, -438.0, 0.0, 0.0, 188.0, 0.0, 0.0),
11363		new NutationModel( 0, 0, 0, 1, 1, -390.0, 0.0, 0.0, 205.0, 0.0, 0.0),
11364		new NutationModel(-1, 0, 2, 2, 0, 639.0, -11.0, -2.0, -19.0, 0.0, 0.0),
11365		new NutationModel( 2, 1, 2, 0, 2, 412.0, 0.0, -2.0, -176.0, 0.0, -1.0),
11366		new NutationModel( 1, 1, 0, 0, 1, -361.0, 0.0, 0.0, 189.0, 0.0, 0.0),
11367		new NutationModel( 1, 1, 2, 0, 1, 360.0, 0.0, -1.0, -185.0, 0.0, -1.0),
11368		new NutationModel( 2, 0, 0, 2, 0, 588.0, 0.0, -3.0, -24.0, 0.0, 0.0),
11369		new NutationModel( 1, 0,-2, 2, 0, -578.0, 0.0, 1.0, 5.0, 0.0, 0.0),
11370		new NutationModel(-1, 0, 0, 2, 2, -396.0, 0.0, 0.0, 171.0, 0.0, 0.0),
11371		new NutationModel( 0, 1, 0, 1, 0, 565.0, 0.0, -1.0, -6.0, 0.0, 0.0),
11372
11373		/* 131-140 */
11374		new NutationModel( 0, 1, 0,-2, 1, -335.0, 0.0, -1.0, 184.0, 0.0, -1.0),
11375		new NutationModel(-1, 0, 2,-2, 2, 357.0, 0.0, 1.0, -154.0, 0.0, 0.0),
11376		new NutationModel( 0, 0, 0,-1, 1, 321.0, 0.0, 1.0, -174.0, 0.0, 0.0),
11377		new NutationModel(-1, 1, 0, 0, 1, -301.0, 0.0, -1.0, 162.0, 0.0, 0.0),
11378		new NutationModel( 1, 0, 2,-1, 2, -334.0, 0.0, 0.0, 144.0, 0.0, 0.0),
11379		new NutationModel( 1,-1, 0, 2, 0, 493.0, 0.0, -2.0, -15.0, 0.0, 0.0),
11380		new NutationModel( 0, 0, 0, 4, 0, 494.0, 0.0, -2.0, -19.0, 0.0, 0.0),
11381		new NutationModel( 1, 0, 2, 1, 2, 337.0, 0.0, -1.0, -143.0, 0.0, -1.0),
11382		new NutationModel( 0, 0, 2, 1, 1, 280.0, 0.0, -1.0, -144.0, 0.0, 0.0),
11383		new NutationModel( 1, 0, 0,-2, 2, 309.0, 0.0, 1.0, -134.0, 0.0, 0.0),
11384
11385		/* 141-150 */
11386		new NutationModel(-1, 0, 2, 4, 1, -263.0, 0.0, 2.0, 131.0, 0.0, 1.0),
11387		new NutationModel( 1, 0,-2, 0, 1, 253.0, 0.0, 1.0, -138.0, 0.0, 0.0),
11388		new NutationModel( 1, 1, 2,-2, 1, 245.0, 0.0, 0.0, -128.0, 0.0, 0.0),
11389		new NutationModel( 0, 0, 2, 2, 0, 416.0, 0.0, -2.0, -17.0, 0.0, 0.0),
11390		new NutationModel(-1, 0, 2,-1, 1, -229.0, 0.0, 0.0, 128.0, 0.0, 0.0),
11391		new NutationModel(-2, 0, 2, 2, 1, 231.0, 0.0, 0.0, -120.0, 0.0, 0.0),
11392		new NutationModel( 4, 0, 2, 0, 2, -259.0, 0.0, 2.0, 109.0, 0.0, 1.0),
11393		new NutationModel( 2,-1, 0, 0, 0, 375.0, 0.0, -1.0, -8.0, 0.0, 0.0),
11394		new NutationModel( 2, 1, 2,-2, 2, 252.0, 0.0, 0.0, -108.0, 0.0, 0.0),
11395		new NutationModel( 0, 1, 2, 1, 2, -245.0, 0.0, 1.0, 104.0, 0.0, 0.0),
11396
11397		/* 151-160 */
11398		new NutationModel( 1, 0, 4,-2, 2, 243.0, 0.0, -1.0, -104.0, 0.0, 0.0),
11399		new NutationModel(-1,-1, 0, 0, 1, 208.0, 0.0, 1.0, -112.0, 0.0, 0.0),
11400		new NutationModel( 0, 1, 0, 2, 1, 199.0, 0.0, 0.0, -102.0, 0.0, 0.0),
11401		new NutationModel(-2, 0, 2, 4, 1, -208.0, 0.0, 1.0, 105.0, 0.0, 0.0),
11402		new NutationModel( 2, 0, 2, 0, 0, 335.0, 0.0, -2.0, -14.0, 0.0, 0.0),
11403		new NutationModel( 1, 0, 0, 1, 0, -325.0, 0.0, 1.0, 7.0, 0.0, 0.0),
11404		new NutationModel(-1, 0, 0, 4, 1, -187.0, 0.0, 0.0, 96.0, 0.0, 0.0),
11405		new NutationModel(-1, 0, 4, 0, 1, 197.0, 0.0, -1.0, -100.0, 0.0, 0.0),
11406		new NutationModel( 2, 0, 2, 2, 1, -192.0, 0.0, 2.0, 94.0, 0.0, 1.0),
11407		new NutationModel( 0, 0, 2,-3, 2, -188.0, 0.0, 0.0, 83.0, 0.0, 0.0),
11408
11409		/* 161-170 */
11410		new NutationModel(-1,-2, 0, 2, 0, 276.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11411		new NutationModel( 2, 1, 0, 0, 0, -286.0, 0.0, 1.0, 6.0, 0.0, 0.0),
11412		new NutationModel( 0, 0, 4, 0, 2, 186.0, 0.0, -1.0, -79.0, 0.0, 0.0),
11413		new NutationModel( 0, 0, 0, 0, 3, -219.0, 0.0, 0.0, 43.0, 0.0, 0.0),
11414		new NutationModel( 0, 3, 0, 0, 0, 276.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11415		new NutationModel( 0, 0, 2,-4, 1, -153.0, 0.0, -1.0, 84.0, 0.0, 0.0),
11416		new NutationModel( 0,-1, 0, 2, 1, -156.0, 0.0, 0.0, 81.0, 0.0, 0.0),
11417		new NutationModel( 0, 0, 0, 4, 1, -154.0, 0.0, 1.0, 78.0, 0.0, 0.0),
11418		new NutationModel(-1,-1, 2, 4, 2, -174.0, 0.0, 1.0, 75.0, 0.0, 0.0),
11419		new NutationModel( 1, 0, 2, 4, 2, -163.0, 0.0, 2.0, 69.0, 0.0, 1.0),
11420
11421		/* 171-180 */
11422		new NutationModel(-2, 2, 0, 2, 0, -228.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11423		new NutationModel(-2,-1, 2, 0, 1, 91.0, 0.0, -4.0, -54.0, 0.0, -2.0),
11424		new NutationModel(-2, 0, 0, 2, 2, 175.0, 0.0, 0.0, -75.0, 0.0, 0.0),
11425		new NutationModel(-1,-1, 2, 0, 2, -159.0, 0.0, 0.0, 69.0, 0.0, 0.0),
11426		new NutationModel( 0, 0, 4,-2, 1, 141.0, 0.0, 0.0, -72.0, 0.0, 0.0),
11427		new NutationModel( 3, 0, 2,-2, 1, 147.0, 0.0, 0.0, -75.0, 0.0, 0.0),
11428		new NutationModel(-2,-1, 0, 2, 1, -132.0, 0.0, 0.0, 69.0, 0.0, 0.0),
11429		new NutationModel( 1, 0, 0,-1, 1, 159.0, 0.0, -28.0, -54.0, 0.0, 11.0),
11430		new NutationModel( 0,-2, 0, 2, 0, 213.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11431		new NutationModel(-2, 0, 0, 4, 1, 123.0, 0.0, 0.0, -64.0, 0.0, 0.0),
11432
11433		/* 181-190 */
11434		new NutationModel(-3, 0, 0, 0, 1, -118.0, 0.0, -1.0, 66.0, 0.0, 0.0),
11435		new NutationModel( 1, 1, 2, 2, 2, 144.0, 0.0, -1.0, -61.0, 0.0, 0.0),
11436		new NutationModel( 0, 0, 2, 4, 1, -121.0, 0.0, 1.0, 60.0, 0.0, 0.0),
11437		new NutationModel( 3, 0, 2, 2, 2, -134.0, 0.0, 1.0, 56.0, 0.0, 1.0),
11438		new NutationModel(-1, 1, 2,-2, 1, -105.0, 0.0, 0.0, 57.0, 0.0, 0.0),
11439		new NutationModel( 2, 0, 0,-4, 1, -102.0, 0.0, 0.0, 56.0, 0.0, 0.0),
11440		new NutationModel( 0, 0, 0,-2, 2, 120.0, 0.0, 0.0, -52.0, 0.0, 0.0),
11441		new NutationModel( 2, 0, 2,-4, 1, 101.0, 0.0, 0.0, -54.0, 0.0, 0.0),
11442		new NutationModel(-1, 1, 0, 2, 1, -113.0, 0.0, 0.0, 59.0, 0.0, 0.0),
11443		new NutationModel( 0, 0, 2,-1, 1, -106.0, 0.0, 0.0, 61.0, 0.0, 0.0),
11444
11445		/* 191-200 */
11446		new NutationModel( 0,-2, 2, 2, 2, -129.0, 0.0, 1.0, 55.0, 0.0, 0.0),
11447		new NutationModel( 2, 0, 0, 2, 1, -114.0, 0.0, 0.0, 57.0, 0.0, 0.0),
11448		new NutationModel( 4, 0, 2,-2, 2, 113.0, 0.0, -1.0, -49.0, 0.0, 0.0),
11449		new NutationModel( 2, 0, 0,-2, 2, -102.0, 0.0, 0.0, 44.0, 0.0, 0.0),
11450		new NutationModel( 0, 2, 0, 0, 1, -94.0, 0.0, 0.0, 51.0, 0.0, 0.0),
11451		new NutationModel( 1, 0, 0,-4, 1, -100.0, 0.0, -1.0, 56.0, 0.0, 0.0),
11452		new NutationModel( 0, 2, 2,-2, 1, 87.0, 0.0, 0.0, -47.0, 0.0, 0.0),
11453		new NutationModel(-3, 0, 0, 4, 0, 161.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11454		new NutationModel(-1, 1, 2, 0, 1, 96.0, 0.0, 0.0, -50.0, 0.0, 0.0),
11455		new NutationModel(-1,-1, 0, 4, 0, 151.0, 0.0, -1.0, -5.0, 0.0, 0.0),
11456
11457		/* 201-210 */
11458		new NutationModel(-1,-2, 2, 2, 2, -104.0, 0.0, 0.0, 44.0, 0.0, 0.0),
11459		new NutationModel(-2,-1, 2, 4, 2, -110.0, 0.0, 0.0, 48.0, 0.0, 0.0),
11460		new NutationModel( 1,-1, 2, 2, 1, -100.0, 0.0, 1.0, 50.0, 0.0, 0.0),
11461		new NutationModel(-2, 1, 0, 2, 0, 92.0, 0.0, -5.0, 12.0, 0.0, -2.0),
11462		new NutationModel(-2, 1, 2, 0, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0),
11463		new NutationModel( 2, 1, 0,-2, 1, 82.0, 0.0, 0.0, -45.0, 0.0, 0.0),
11464		new NutationModel(-3, 0, 2, 0, 1, -78.0, 0.0, 0.0, 41.0, 0.0, 0.0),
11465		new NutationModel(-2, 0, 2,-2, 1, -77.0, 0.0, 0.0, 43.0, 0.0, 0.0),
11466		new NutationModel(-1, 1, 0, 2, 2, 2.0, 0.0, 0.0, 54.0, 0.0, 0.0),
11467		new NutationModel( 0,-1, 2,-1, 2, 94.0, 0.0, 0.0, -40.0, 0.0, 0.0),
11468
11469		/* 211-220 */
11470		new NutationModel(-1, 0, 4,-2, 2, -93.0, 0.0, 0.0, 40.0, 0.0, 0.0),
11471		new NutationModel( 0,-2, 2, 0, 2, -83.0, 0.0, 10.0, 40.0, 0.0, -2.0),
11472		new NutationModel(-1, 0, 2, 1, 2, 83.0, 0.0, 0.0, -36.0, 0.0, 0.0),
11473		new NutationModel( 2, 0, 0, 0, 2, -91.0, 0.0, 0.0, 39.0, 0.0, 0.0),
11474		new NutationModel( 0, 0, 2, 0, 3, 128.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11475		new NutationModel(-2, 0, 4, 0, 2, -79.0, 0.0, 0.0, 34.0, 0.0, 0.0),
11476		new NutationModel(-1, 0,-2, 0, 1, -83.0, 0.0, 0.0, 47.0, 0.0, 0.0),
11477		new NutationModel(-1, 1, 2, 2, 1, 84.0, 0.0, 0.0, -44.0, 0.0, 0.0),
11478		new NutationModel( 3, 0, 0, 0, 1, 83.0, 0.0, 0.0, -43.0, 0.0, 0.0),
11479		new NutationModel(-1, 0, 2, 3, 2, 91.0, 0.0, 0.0, -39.0, 0.0, 0.0),
11480
11481		/* 221-230 */
11482		new NutationModel( 2,-1, 2, 0, 1, -77.0, 0.0, 0.0, 39.0, 0.0, 0.0),
11483		new NutationModel( 0, 1, 2, 2, 1, 84.0, 0.0, 0.0, -43.0, 0.0, 0.0),
11484		new NutationModel( 0,-1, 2, 4, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0),
11485		new NutationModel( 2,-1, 2, 2, 2, -92.0, 0.0, 1.0, 39.0, 0.0, 0.0),
11486		new NutationModel( 0, 2,-2, 2, 0, -94.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11487		new NutationModel(-1,-1, 2,-1, 1, 68.0, 0.0, 0.0, -36.0, 0.0, 0.0),
11488		new NutationModel( 0,-2, 0, 0, 1, -61.0, 0.0, 0.0, 32.0, 0.0, 0.0),
11489		new NutationModel( 1, 0, 2,-4, 2, 71.0, 0.0, 0.0, -31.0, 0.0, 0.0),
11490		new NutationModel( 1,-1, 0,-2, 1, 62.0, 0.0, 0.0, -34.0, 0.0, 0.0),
11491		new NutationModel(-1,-1, 2, 0, 1, -63.0, 0.0, 0.0, 33.0, 0.0, 0.0),
11492
11493		/* 231-240 */
11494		new NutationModel( 1,-1, 2,-2, 2, -73.0, 0.0, 0.0, 32.0, 0.0, 0.0),
11495		new NutationModel(-2,-1, 0, 4, 0, 115.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11496		new NutationModel(-1, 0, 0, 3, 0, -103.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11497		new NutationModel(-2,-1, 2, 2, 2, 63.0, 0.0, 0.0, -28.0, 0.0, 0.0),
11498		new NutationModel( 0, 2, 2, 0, 2, 74.0, 0.0, 0.0, -32.0, 0.0, 0.0),
11499		new NutationModel( 1, 1, 0, 2, 0, -103.0, 0.0, -3.0, 3.0, 0.0, -1.0),
11500		new NutationModel( 2, 0, 2,-1, 2, -69.0, 0.0, 0.0, 30.0, 0.0, 0.0),
11501		new NutationModel( 1, 0, 2, 1, 1, 57.0, 0.0, 0.0, -29.0, 0.0, 0.0),
11502		new NutationModel( 4, 0, 0, 0, 0, 94.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11503		new NutationModel( 2, 1, 2, 0, 1, 64.0, 0.0, 0.0, -33.0, 0.0, 0.0),
11504
11505		/* 241-250 */
11506		new NutationModel( 3,-1, 2, 0, 2, -63.0, 0.0, 0.0, 26.0, 0.0, 0.0),
11507		new NutationModel(-2, 2, 0, 2, 1, -38.0, 0.0, 0.0, 20.0, 0.0, 0.0),
11508		new NutationModel( 1, 0, 2,-3, 1, -43.0, 0.0, 0.0, 24.0, 0.0, 0.0),
11509		new NutationModel( 1, 1, 2,-4, 1, -45.0, 0.0, 0.0, 23.0, 0.0, 0.0),
11510		new NutationModel(-1,-1, 2,-2, 1, 47.0, 0.0, 0.0, -24.0, 0.0, 0.0),
11511		new NutationModel( 0,-1, 0,-1, 1, -48.0, 0.0, 0.0, 25.0, 0.0, 0.0),
11512		new NutationModel( 0,-1, 0,-2, 1, 45.0, 0.0, 0.0, -26.0, 0.0, 0.0),
11513		new NutationModel(-2, 0, 0, 0, 2, 56.0, 0.0, 0.0, -25.0, 0.0, 0.0),
11514		new NutationModel(-2, 0,-2, 2, 0, 88.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11515		new NutationModel(-1, 0,-2, 4, 0, -75.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11516
11517		/* 251-260 */
11518		new NutationModel( 1,-2, 0, 0, 0, 85.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11519		new NutationModel( 0, 1, 0, 1, 1, 49.0, 0.0, 0.0, -26.0, 0.0, 0.0),
11520		new NutationModel(-1, 2, 0, 2, 0, -74.0, 0.0, -3.0, -1.0, 0.0, -1.0),
11521		new NutationModel( 1,-1, 2,-2, 1, -39.0, 0.0, 0.0, 21.0, 0.0, 0.0),
11522		new NutationModel( 1, 2, 2,-2, 2, 45.0, 0.0, 0.0, -20.0, 0.0, 0.0),
11523		new NutationModel( 2,-1, 2,-2, 2, 51.0, 0.0, 0.0, -22.0, 0.0, 0.0),
11524		new NutationModel( 1, 0, 2,-1, 1, -40.0, 0.0, 0.0, 21.0, 0.0, 0.0),
11525		new NutationModel( 2, 1, 2,-2, 1, 41.0, 0.0, 0.0, -21.0, 0.0, 0.0),
11526		new NutationModel(-2, 0, 0,-2, 1, -42.0, 0.0, 0.0, 24.0, 0.0, 0.0),
11527		new NutationModel( 1,-2, 2, 0, 2, -51.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11528
11529		/* 261-270 */
11530		new NutationModel( 0, 1, 2, 1, 1, -42.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11531		new NutationModel( 1, 0, 4,-2, 1, 39.0, 0.0, 0.0, -21.0, 0.0, 0.0),
11532		new NutationModel(-2, 0, 4, 2, 2, 46.0, 0.0, 0.0, -18.0, 0.0, 0.0),
11533		new NutationModel( 1, 1, 2, 1, 2, -53.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11534		new NutationModel( 1, 0, 0, 4, 0, 82.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11535		new NutationModel( 1, 0, 2, 2, 0, 81.0, 0.0, -1.0, -4.0, 0.0, 0.0),
11536		new NutationModel( 2, 0, 2, 1, 2, 47.0, 0.0, 0.0, -19.0, 0.0, 0.0),
11537		new NutationModel( 3, 1, 2, 0, 2, 53.0, 0.0, 0.0, -23.0, 0.0, 0.0),
11538		new NutationModel( 4, 0, 2, 0, 1, -45.0, 0.0, 0.0, 22.0, 0.0, 0.0),
11539		new NutationModel(-2,-1, 2, 0, 0, -44.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11540
11541		/* 271-280 */
11542		new NutationModel( 0, 1,-2, 2, 1, -33.0, 0.0, 0.0, 16.0, 0.0, 0.0),
11543		new NutationModel( 1, 0,-2, 1, 0, -61.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11544		new NutationModel( 0,-1,-2, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11545		new NutationModel( 2,-1, 0,-2, 1, -38.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11546		new NutationModel(-1, 0, 2,-1, 2, -33.0, 0.0, 0.0, 21.0, 0.0, 0.0),
11547		new NutationModel( 1, 0, 2,-3, 2, -60.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11548		new NutationModel( 0, 1, 2,-2, 3, 48.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11549		new NutationModel( 0, 0, 2,-3, 1, 27.0, 0.0, 0.0, -14.0, 0.0, 0.0),
11550		new NutationModel(-1, 0,-2, 2, 1, 38.0, 0.0, 0.0, -20.0, 0.0, 0.0),
11551		new NutationModel( 0, 0, 2,-4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11552
11553		/* 281-290 */
11554		new NutationModel(-2, 1, 0, 0, 1, -29.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11555		new NutationModel(-1, 0, 0,-1, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11556		new NutationModel( 2, 0, 2,-4, 2, -32.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11557		new NutationModel( 0, 0, 4,-4, 4, 45.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11558		new NutationModel( 0, 0, 4,-4, 2, -44.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11559		new NutationModel(-1,-2, 0, 2, 1, 28.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11560		new NutationModel(-2, 0, 0, 3, 0, -51.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11561		new NutationModel( 1, 0,-2, 2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0),
11562		new NutationModel(-3, 0, 2, 2, 2, 44.0, 0.0, 0.0, -19.0, 0.0, 0.0),
11563		new NutationModel(-3, 0, 2, 2, 1, 26.0, 0.0, 0.0, -14.0, 0.0, 0.0),
11564
11565		/* 291-300 */
11566		new NutationModel(-2, 0, 2, 2, 0, -60.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11567		new NutationModel( 2,-1, 0, 0, 1, 35.0, 0.0, 0.0, -18.0, 0.0, 0.0),
11568		new NutationModel(-2, 1, 2, 2, 2, -27.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11569		new NutationModel( 1, 1, 0, 1, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11570		new NutationModel( 0, 1, 4,-2, 2, 36.0, 0.0, 0.0, -15.0, 0.0, 0.0),
11571		new NutationModel(-1, 1, 0,-2, 1, -36.0, 0.0, 0.0, 20.0, 0.0, 0.0),
11572		new NutationModel( 0, 0, 0,-4, 1, -35.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11573		new NutationModel( 1,-1, 0, 2, 1, -37.0, 0.0, 0.0, 19.0, 0.0, 0.0),
11574		new NutationModel( 1, 1, 0, 2, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11575		new NutationModel(-1, 2, 2, 2, 2, 35.0, 0.0, 0.0, -14.0, 0.0, 0.0),
11576
11577		/* 301-310 */
11578		new NutationModel( 3, 1, 2,-2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11579		new NutationModel( 0,-1, 0, 4, 0, 65.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11580		new NutationModel( 2,-1, 0, 2, 0, 47.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11581		new NutationModel( 0, 0, 4, 0, 1, 32.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11582		new NutationModel( 2, 0, 4,-2, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11583		new NutationModel(-1,-1, 2, 4, 1, -30.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11584		new NutationModel( 1, 0, 0, 4, 1, -32.0, 0.0, 0.0, 16.0, 0.0, 0.0),
11585		new NutationModel( 1,-2, 2, 2, 2, -31.0, 0.0, 0.0, 13.0, 0.0, 0.0),
11586		new NutationModel( 0, 0, 2, 3, 2, 37.0, 0.0, 0.0, -16.0, 0.0, 0.0),
11587		new NutationModel(-1, 1, 2, 4, 2, 31.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11588
11589		/* 311-320 */
11590		new NutationModel( 3, 0, 0, 2, 0, 49.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11591		new NutationModel(-1, 0, 4, 2, 2, 32.0, 0.0, 0.0, -13.0, 0.0, 0.0),
11592		new NutationModel( 1, 1, 2, 2, 1, 23.0, 0.0, 0.0, -12.0, 0.0, 0.0),
11593		new NutationModel(-2, 0, 2, 6, 2, -43.0, 0.0, 0.0, 18.0, 0.0, 0.0),
11594		new NutationModel( 2, 1, 2, 2, 2, 26.0, 0.0, 0.0, -11.0, 0.0, 0.0),
11595		new NutationModel(-1, 0, 2, 6, 2, -32.0, 0.0, 0.0, 14.0, 0.0, 0.0),
11596		new NutationModel( 1, 0, 2, 4, 1, -29.0, 0.0, 0.0, 14.0, 0.0, 0.0),
11597		new NutationModel( 2, 0, 2, 4, 2, -27.0, 0.0, 0.0, 12.0, 0.0, 0.0),
11598		new NutationModel( 1, 1,-2, 1, 0, 30.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11599		new NutationModel(-3, 1, 2, 1, 2, -11.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11600
11601		/* 321-330 */
11602		new NutationModel( 2, 0,-2, 0, 2, -21.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11603		new NutationModel(-1, 0, 0, 1, 2, -34.0, 0.0, 0.0, 15.0, 0.0, 0.0),
11604		new NutationModel(-4, 0, 2, 2, 1, -10.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11605		new NutationModel(-1,-1, 0, 1, 0, -36.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11606		new NutationModel( 0, 0,-2, 2, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11607		new NutationModel( 1, 0, 0,-1, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11608		new NutationModel( 0,-1, 2,-2, 3, -21.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11609		new NutationModel(-2, 1, 2, 0, 0, -29.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11610		new NutationModel( 0, 0, 2,-2, 4, -15.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11611		new NutationModel(-2,-2, 0, 2, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11612
11613		/* 331-340 */
11614		new NutationModel(-2, 0,-2, 4, 0, 28.0, 0.0, 0.0, 0.0, 0.0, -2.0),
11615		new NutationModel( 0,-2,-2, 2, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11616		new NutationModel( 1, 2, 0,-2, 1, -22.0, 0.0, 0.0, 12.0, 0.0, 0.0),
11617		new NutationModel( 3, 0, 0,-4, 1, -14.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11618		new NutationModel(-1, 1, 2,-2, 2, 24.0, 0.0, 0.0, -11.0, 0.0, 0.0),
11619		new NutationModel( 1,-1, 2,-4, 1, 11.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11620		new NutationModel( 1, 1, 0,-2, 2, 14.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11621		new NutationModel(-3, 0, 2, 0, 0, 24.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11622		new NutationModel(-3, 0, 2, 0, 2, 18.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11623		new NutationModel(-2, 0, 0, 1, 0, -38.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11624
11625		/* 341-350 */
11626		new NutationModel( 0, 0,-2, 1, 0, -31.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11627		new NutationModel(-3, 0, 0, 2, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11628		new NutationModel(-1,-1,-2, 2, 0, 29.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11629		new NutationModel( 0, 1, 2,-4, 1, -18.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11630		new NutationModel( 2, 1, 0,-4, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11631		new NutationModel( 0, 2, 0,-2, 1, -17.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11632		new NutationModel( 1, 0, 0,-3, 1, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11633		new NutationModel(-2, 0, 2,-2, 2, 16.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11634		new NutationModel(-2,-1, 0, 0, 1, 22.0, 0.0, 0.0, -12.0, 0.0, 0.0),
11635		new NutationModel(-4, 0, 0, 2, 0, 20.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11636
11637		/* 351-360 */
11638		new NutationModel( 1, 1, 0,-4, 1, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11639		new NutationModel(-1, 0, 2,-4, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11640		new NutationModel( 0, 0, 4,-4, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11641		new NutationModel( 0, 3, 2,-2, 2, 0.0, 0.0, 0.0, -7.0, 0.0, 0.0),
11642		new NutationModel(-3,-1, 0, 4, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11643		new NutationModel(-3, 0, 0, 4, 1, 19.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11644		new NutationModel( 1,-1,-2, 2, 0, -34.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11645		new NutationModel(-1,-1, 0, 2, 2, -20.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11646		new NutationModel( 1,-2, 0, 0, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11647		new NutationModel( 1,-1, 0, 0, 2, -18.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11648
11649		/* 361-370 */
11650		new NutationModel( 0, 0, 0, 1, 2, 13.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11651		new NutationModel(-1,-1, 2, 0, 0, 17.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11652		new NutationModel( 1,-2, 2,-2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11653		new NutationModel( 0,-1, 2,-1, 1, 15.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11654		new NutationModel(-1, 0, 2, 0, 3, -11.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11655		new NutationModel( 1, 1, 0, 0, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11656		new NutationModel(-1, 1, 2, 0, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11657		new NutationModel( 1, 2, 0, 0, 0, -35.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11658		new NutationModel(-1, 2, 2, 0, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11659		new NutationModel(-1, 0, 4,-2, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11660
11661		/* 371-380 */
11662		new NutationModel( 3, 0, 2,-4, 2, -26.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11663		new NutationModel( 1, 2, 2,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11664		new NutationModel( 1, 0, 4,-4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11665		new NutationModel(-2,-1, 0, 4, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11666		new NutationModel( 0,-1, 0, 2, 2, -21.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11667		new NutationModel(-2, 1, 0, 4, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11668		new NutationModel(-2,-1, 2, 2, 1, 9.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11669		new NutationModel( 2, 0,-2, 2, 0, -29.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11670		new NutationModel( 1, 0, 0, 1, 1, -19.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11671		new NutationModel( 0, 1, 0, 2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11672
11673		/* 381-390 */
11674		new NutationModel( 1,-1, 2,-1, 2, 22.0, 0.0, 0.0, -9.0, 0.0, 0.0),
11675		new NutationModel(-2, 0, 4, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11676		new NutationModel( 2, 1, 0, 0, 1, -20.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11677		new NutationModel( 0, 1, 2, 0, 0, -20.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11678		new NutationModel( 0,-1, 4,-2, 2, -17.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11679		new NutationModel( 0, 0, 4,-2, 4, 15.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11680		new NutationModel( 0, 2, 2, 0, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11681		new NutationModel(-3, 0, 0, 6, 0, 14.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11682		new NutationModel(-1,-1, 0, 4, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11683		new NutationModel( 1,-2, 0, 2, 0, 25.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11684
11685		/* 391-400 */
11686		new NutationModel(-1, 0, 0, 4, 2, -13.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11687		new NutationModel(-1,-2, 2, 2, 1, -14.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11688		new NutationModel(-1, 0, 0,-2, 2, 13.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11689		new NutationModel( 1, 0,-2,-2, 1, -17.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11690		new NutationModel( 0, 0,-2,-2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11691		new NutationModel(-2, 0,-2, 0, 1, -10.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11692		new NutationModel( 0, 0, 0, 3, 1, 10.0, 0.0, 0.0, -6.0, 0.0, 0.0),
11693		new NutationModel( 0, 0, 0, 3, 0, -15.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11694		new NutationModel(-1, 1, 0, 4, 0, -22.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11695		new NutationModel(-1,-1, 2, 2, 0, 28.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11696
11697		/* 401-410 */
11698		new NutationModel(-2, 0, 2, 3, 2, 15.0, 0.0, 0.0, -7.0, 0.0, 0.0),
11699		new NutationModel( 1, 0, 0, 2, 2, 23.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11700		new NutationModel( 0,-1, 2, 1, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11701		new NutationModel( 3,-1, 0, 0, 0, 29.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11702		new NutationModel( 2, 0, 0, 1, 0, -25.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11703		new NutationModel( 1,-1, 2, 0, 0, 22.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11704		new NutationModel( 0, 0, 2, 1, 0, -18.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11705		new NutationModel( 1, 0, 2, 0, 3, 15.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11706		new NutationModel( 3, 1, 0, 0, 0, -23.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11707		new NutationModel( 3,-1, 2,-2, 2, 12.0, 0.0, 0.0, -5.0, 0.0, 0.0),
11708
11709		/* 411-420 */
11710		new NutationModel( 2, 0, 2,-1, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11711		new NutationModel( 1, 1, 2, 0, 0, -19.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11712		new NutationModel( 0, 0, 4,-1, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11713		new NutationModel( 1, 2, 2, 0, 2, 21.0, 0.0, 0.0, -9.0, 0.0, 0.0),
11714		new NutationModel(-2, 0, 0, 6, 0, 23.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11715		new NutationModel( 0,-1, 0, 4, 1, -16.0, 0.0, 0.0, 8.0, 0.0, 0.0),
11716		new NutationModel(-2,-1, 2, 4, 1, -19.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11717		new NutationModel( 0,-2, 2, 2, 1, -22.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11718		new NutationModel( 0,-1, 2, 2, 0, 27.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11719		new NutationModel(-1, 0, 2, 3, 1, 16.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11720
11721		/* 421-430 */
11722		new NutationModel(-2, 1, 2, 4, 2, 19.0, 0.0, 0.0, -8.0, 0.0, 0.0),
11723		new NutationModel( 2, 0, 0, 2, 2, 9.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11724		new NutationModel( 2,-2, 2, 0, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11725		new NutationModel(-1, 1, 2, 3, 2, -9.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11726		new NutationModel( 3, 0, 2,-1, 2, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11727		new NutationModel( 4, 0, 2,-2, 1, 18.0, 0.0, 0.0, -9.0, 0.0, 0.0),
11728		new NutationModel(-1, 0, 0, 6, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11729		new NutationModel(-1,-2, 2, 4, 2, -10.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11730		new NutationModel(-3, 0, 2, 6, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11731		new NutationModel(-1, 0, 2, 4, 0, 16.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11732
11733		/* 431-440 */
11734		new NutationModel( 3, 0, 0, 2, 1, -12.0, 0.0, 0.0, 6.0, 0.0, 0.0),
11735		new NutationModel( 3,-1, 2, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11736		new NutationModel( 3, 0, 2, 0, 0, 30.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11737		new NutationModel( 1, 0, 4, 0, 2, 24.0, 0.0, 0.0, -10.0, 0.0, 0.0),
11738		new NutationModel( 5, 0, 2,-2, 2, 10.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11739		new NutationModel( 0,-1, 2, 4, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11740		new NutationModel( 2,-1, 2, 2, 1, -16.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11741		new NutationModel( 0, 1, 2, 4, 2, 17.0, 0.0, 0.0, -7.0, 0.0, 0.0),
11742		new NutationModel( 1,-1, 2, 4, 2, -24.0, 0.0, 0.0, 10.0, 0.0, 0.0),
11743		new NutationModel( 3,-1, 2, 2, 2, -12.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11744
11745		/* 441-450 */
11746		new NutationModel( 3, 0, 2, 2, 1, -24.0, 0.0, 0.0, 11.0, 0.0, 0.0),
11747		new NutationModel( 5, 0, 2, 0, 2, -23.0, 0.0, 0.0, 9.0, 0.0, 0.0),
11748		new NutationModel( 0, 0, 2, 6, 2, -13.0, 0.0, 0.0, 5.0, 0.0, 0.0),
11749		new NutationModel( 4, 0, 2, 2, 2, -15.0, 0.0, 0.0, 7.0, 0.0, 0.0),
11750		new NutationModel( 0,-1, 1,-1, 1, 0.0, 0.0,-1988.0, 0.0, 0.0,-1679.0),
11751		new NutationModel(-1, 0, 1, 0, 3, 0.0, 0.0, -63.0, 0.0, 0.0, -27.0),
11752		new NutationModel( 0,-2, 2,-2, 3, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11753		new NutationModel( 1, 0,-1, 0, 1, 0.0, 0.0, 5.0, 0.0, 0.0, 4.0),
11754		new NutationModel( 2,-2, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11755		new NutationModel(-1, 0, 1, 0, 2, 0.0, 0.0, 364.0, 0.0, 0.0, 176.0),
11756
11757		/* 451-460 */
11758		new NutationModel(-1, 0, 1, 0, 1, 0.0, 0.0,-1044.0, 0.0, 0.0, -891.0),
11759		new NutationModel(-1,-1, 2,-1, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11760		new NutationModel(-2, 2, 0, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11761		new NutationModel(-1, 0, 1, 0, 0, 0.0, 0.0, 330.0, 0.0, 0.0, 0.0),
11762		new NutationModel(-4, 1, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11763		new NutationModel(-3, 0, 2, 1, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11764		new NutationModel(-2,-1, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11765		new NutationModel( 1, 0,-2, 1, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11766		new NutationModel( 2,-1,-2, 0, 1, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11767		new NutationModel(-4, 0, 2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11768
11769		/* 461-470 */
11770		new NutationModel(-3, 1, 0, 3, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11771		new NutationModel(-1, 0,-1, 2, 0, 0.0, 0.0, 5.0, 0.0, 0.0, 0.0),
11772		new NutationModel( 0,-2, 0, 0, 2, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11773		new NutationModel( 0,-2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11774		new NutationModel(-3, 0, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11775		new NutationModel(-2,-1, 0, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11776		new NutationModel(-1, 0,-2, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11777		new NutationModel(-4, 0, 0, 4, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11778		new NutationModel( 2, 1,-2, 0, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11779		new NutationModel( 2,-1, 0,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11780
11781		/* 471-480 */
11782		new NutationModel( 0, 0, 1,-1, 0, -5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11783		new NutationModel(-1, 2, 0, 1, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11784		new NutationModel(-2, 1, 2, 0, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11785		new NutationModel( 1, 1, 0,-1, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11786		new NutationModel( 1, 0, 1,-2, 1, 0.0, 0.0, -12.0, 0.0, 0.0, -10.0),
11787		new NutationModel( 0, 2, 0, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11788		new NutationModel( 1,-1, 2,-3, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11789		new NutationModel(-1, 1, 2,-1, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11790		new NutationModel(-2, 0, 4,-2, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11791		new NutationModel(-2, 0, 4,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11792
11793		/* 481-490 */
11794		new NutationModel(-2,-2, 0, 2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11795		new NutationModel(-2, 0,-2, 4, 0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11796		new NutationModel( 1, 2, 2,-4, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11797		new NutationModel( 1, 1, 2,-4, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11798		new NutationModel(-1, 2, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11799		new NutationModel( 2, 0, 0,-3, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11800		new NutationModel(-1, 2, 0, 0, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11801		new NutationModel( 0, 0, 0,-2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11802		new NutationModel(-1,-1, 2,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11803		new NutationModel(-1, 1, 0, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11804
11805		/* 491-500 */
11806		new NutationModel( 0, 0, 0,-1, 2, -8.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11807		new NutationModel(-2, 1, 0, 1, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11808		new NutationModel( 1,-2, 0,-2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11809		new NutationModel( 1, 0,-2, 0, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11810		new NutationModel(-3, 1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11811		new NutationModel(-1, 1,-2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11812		new NutationModel(-1,-1, 0, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11813		new NutationModel(-3, 0, 0, 2, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11814		new NutationModel(-3,-1, 0, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11815		new NutationModel( 2, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11816
11817		/* 501-510 */
11818		new NutationModel( 0, 1, 2,-4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11819		new NutationModel( 2, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11820		new NutationModel(-2, 1, 2,-2, 1, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11821		new NutationModel( 0,-1, 2,-4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11822		new NutationModel( 0, 1, 0,-2, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11823		new NutationModel(-1, 0, 0,-2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11824		new NutationModel( 2, 0,-2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11825		new NutationModel(-4, 0, 2, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11826		new NutationModel(-1,-1, 0,-1, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11827		new NutationModel( 0, 0,-2, 0, 2, 9.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11828
11829		/* 511-520 */
11830		new NutationModel(-3, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11831		new NutationModel(-1, 0,-2, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11832		new NutationModel(-2, 0,-2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11833		new NutationModel( 0, 0,-4, 2, 0, 8.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11834		new NutationModel(-2,-1,-2, 2, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11835		new NutationModel( 1, 0, 2,-6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11836		new NutationModel(-1, 0, 2,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11837		new NutationModel( 1, 0, 0,-4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11838		new NutationModel( 2, 1, 2,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11839		new NutationModel( 2, 1, 2,-4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11840
11841		/* 521-530 */
11842		new NutationModel( 0, 1, 4,-4, 4, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11843		new NutationModel( 0, 1, 4,-4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11844		new NutationModel(-1,-1,-2, 4, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11845		new NutationModel(-1,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11846		new NutationModel(-1, 0,-2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11847		new NutationModel(-2,-1, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11848		new NutationModel( 0, 0,-2, 3, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11849		new NutationModel(-2, 0, 0, 3, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11850		new NutationModel( 0,-1, 0, 1, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11851		new NutationModel(-3, 0, 2, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11852
11853		/* 531-540 */
11854		new NutationModel( 1, 1,-2, 2, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11855		new NutationModel(-1, 1, 0, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11856		new NutationModel( 1,-2, 2,-2, 1, 10.0, 0.0, 13.0, 6.0, 0.0, -5.0),
11857		new NutationModel( 0, 0, 1, 0, 2, 0.0, 0.0, 30.0, 0.0, 0.0, 14.0),
11858		new NutationModel( 0, 0, 1, 0, 1, 0.0, 0.0, -162.0, 0.0, 0.0, -138.0),
11859		new NutationModel( 0, 0, 1, 0, 0, 0.0, 0.0, 75.0, 0.0, 0.0, 0.0),
11860		new NutationModel(-1, 2, 0, 2, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11861		new NutationModel( 0, 0, 2, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11862		new NutationModel(-2, 0, 2, 0, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11863		new NutationModel( 2, 0, 0,-1, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11864
11865		/* 541-550 */
11866		new NutationModel( 3, 0, 0,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11867		new NutationModel( 1, 0, 2,-2, 3, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11868		new NutationModel( 1, 2, 0, 0, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11869		new NutationModel( 2, 0, 2,-3, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11870		new NutationModel(-1, 1, 4,-2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11871		new NutationModel(-2,-2, 0, 4, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11872		new NutationModel( 0,-3, 0, 2, 0, 9.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11873		new NutationModel( 0, 0,-2, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11874		new NutationModel(-1,-1, 0, 3, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11875		new NutationModel(-2, 0, 0, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11876
11877		/* 551-560 */
11878		new NutationModel(-1, 0, 0, 3, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11879		new NutationModel( 2,-2, 0, 0, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11880		new NutationModel( 1,-1, 0, 1, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11881		new NutationModel(-1, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11882		new NutationModel( 0,-2, 2, 0, 1, -6.0, 0.0, -3.0, 3.0, 0.0, 1.0),
11883		new NutationModel(-1, 0, 1, 2, 1, 0.0, 0.0, -3.0, 0.0, 0.0, -2.0),
11884		new NutationModel(-1, 1, 0, 3, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11885		new NutationModel(-1,-1, 2, 1, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11886		new NutationModel( 0,-1, 2, 0, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11887		new NutationModel(-2, 1, 2, 2, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11888
11889		/* 561-570 */
11890		new NutationModel( 2,-2, 2,-2, 2, -1.0, 0.0, 3.0, 3.0, 0.0, -1.0),
11891		new NutationModel( 1, 1, 0, 1, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11892		new NutationModel( 1, 0, 1, 0, 1, 0.0, 0.0, -13.0, 0.0, 0.0, -11.0),
11893		new NutationModel( 1, 0, 1, 0, 0, 3.0, 0.0, 6.0, 0.0, 0.0, 0.0),
11894		new NutationModel( 0, 2, 0, 2, 0, -7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11895		new NutationModel( 2,-1, 2,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11896		new NutationModel( 0,-1, 4,-2, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11897		new NutationModel( 0, 0, 4,-2, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11898		new NutationModel( 0, 1, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11899		new NutationModel( 4, 0, 2,-4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11900
11901		/* 571-580 */
11902		new NutationModel( 2, 2, 2,-2, 2, 8.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11903		new NutationModel( 2, 0, 4,-4, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11904		new NutationModel(-1,-2, 0, 4, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11905		new NutationModel(-1,-3, 2, 2, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11906		new NutationModel(-3, 0, 2, 4, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11907		new NutationModel(-3, 0, 2,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11908		new NutationModel(-1,-1, 0,-2, 1, 8.0, 0.0, 0.0, -4.0, 0.0, 0.0),
11909		new NutationModel(-3, 0, 0, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11910		new NutationModel(-3, 0,-2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11911		new NutationModel( 0, 1, 0,-4, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11912
11913		/* 581-590 */
11914		new NutationModel(-2, 1, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11915		new NutationModel(-4, 0, 0, 0, 1, -8.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11916		new NutationModel(-1, 0, 0,-4, 1, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11917		new NutationModel(-3, 0, 0,-2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11918		new NutationModel( 0, 0, 0, 3, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11919		new NutationModel(-1, 1, 0, 4, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11920		new NutationModel( 1,-2, 2, 0, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11921		new NutationModel( 0, 1, 0, 3, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11922		new NutationModel(-1, 0, 2, 2, 3, 6.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11923		new NutationModel( 0, 0, 2, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11924
11925		/* 591-600 */
11926		new NutationModel(-2, 0, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11927		new NutationModel(-1, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11928		new NutationModel( 3, 0, 0, 0, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11929		new NutationModel( 2, 1, 0, 1, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11930		new NutationModel( 2,-1, 2,-1, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11931		new NutationModel( 0, 0, 2, 0, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11932		new NutationModel( 0, 0, 3, 0, 3, 0.0, 0.0, -26.0, 0.0, 0.0, -11.0),
11933		new NutationModel( 0, 0, 3, 0, 2, 0.0, 0.0, -10.0, 0.0, 0.0, -5.0),
11934		new NutationModel(-1, 2, 2, 2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11935		new NutationModel(-1, 0, 4, 0, 0, -13.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11936
11937		/* 601-610 */
11938		new NutationModel( 1, 2, 2, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11939		new NutationModel( 3, 1, 2,-2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11940		new NutationModel( 1, 1, 4,-2, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11941		new NutationModel(-2,-1, 0, 6, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11942		new NutationModel( 0,-2, 0, 4, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11943		new NutationModel(-2, 0, 0, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11944		new NutationModel(-2,-2, 2, 4, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11945		new NutationModel( 0,-3, 2, 2, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11946		new NutationModel( 0, 0, 0, 4, 2, -7.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11947		new NutationModel(-1,-1, 2, 3, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11948
11949		/* 611-620 */
11950		new NutationModel(-2, 0, 2, 4, 0, 13.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11951		new NutationModel( 2,-1, 0, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11952		new NutationModel( 1, 0, 0, 3, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11953		new NutationModel( 0, 1, 0, 4, 1, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11954		new NutationModel( 0, 1, 0, 4, 0, -11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11955		new NutationModel( 1,-1, 2, 1, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11956		new NutationModel( 0, 0, 2, 2, 3, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11957		new NutationModel( 1, 0, 2, 2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11958		new NutationModel(-1, 0, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11959		new NutationModel(-2, 0, 4, 2, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11960
11961		/* 621-630 */
11962		new NutationModel( 2, 1, 0, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11963		new NutationModel( 2, 1, 0, 2, 0, -12.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11964		new NutationModel( 2,-1, 2, 0, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11965		new NutationModel( 1, 0, 2, 1, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11966		new NutationModel( 0, 1, 2, 2, 0, -4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11967		new NutationModel( 2, 0, 2, 0, 3, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11968		new NutationModel( 3, 0, 2, 0, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11969		new NutationModel( 1, 0, 2, 0, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11970		new NutationModel( 1, 0, 3, 0, 3, 0.0, 0.0, -5.0, 0.0, 0.0, -2.0),
11971		new NutationModel( 1, 1, 2, 1, 1, -7.0, 0.0, 0.0, 4.0, 0.0, 0.0),
11972
11973		/* 631-640 */
11974		new NutationModel( 0, 2, 2, 2, 2, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11975		new NutationModel( 2, 1, 2, 0, 0, -3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11976		new NutationModel( 2, 0, 4,-2, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11977		new NutationModel( 4, 1, 2,-2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11978		new NutationModel(-1,-1, 0, 6, 0, 3.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11979		new NutationModel(-3,-1, 2, 6, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
11980		new NutationModel(-1, 0, 0, 6, 1, -5.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11981		new NutationModel(-3, 0, 2, 6, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11982		new NutationModel( 1,-1, 0, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11983		new NutationModel( 1,-1, 0, 4, 0, 12.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11984
11985		/* 641-650 */
11986		new NutationModel(-2, 0, 2, 5, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
11987		new NutationModel( 1,-2, 2, 2, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
11988		new NutationModel( 3,-1, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11989		new NutationModel( 1,-1, 2, 2, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11990		new NutationModel( 0, 0, 2, 3, 1, 5.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11991		new NutationModel(-1, 1, 2, 4, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11992		new NutationModel( 0, 1, 2, 3, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11993		new NutationModel(-1, 0, 4, 2, 1, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
11994		new NutationModel( 2, 0, 2, 1, 1, 6.0, 0.0, 0.0, -3.0, 0.0, 0.0),
11995		new NutationModel( 5, 0, 0, 0, 0, 6.0, 0.0, 0.0, 0.0, 0.0, 0.0),
11996
11997		/* 651-660 */
11998		new NutationModel( 2, 1, 2, 1, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
11999		new NutationModel( 1, 0, 4, 0, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12000		new NutationModel( 3, 1, 2, 0, 1, 7.0, 0.0, 0.0, -4.0, 0.0, 0.0),
12001		new NutationModel( 3, 0, 4,-2, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12002		new NutationModel(-2,-1, 2, 6, 2, -5.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12003		new NutationModel( 0, 0, 0, 6, 0, 5.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12004		new NutationModel( 0,-2, 2, 4, 2, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
12005		new NutationModel(-2, 0, 2, 6, 1, -6.0, 0.0, 0.0, 3.0, 0.0, 0.0),
12006		new NutationModel( 2, 0, 0, 4, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12007		new NutationModel( 2, 0, 0, 4, 0, 10.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12008
12009		/* 661-670 */
12010		new NutationModel( 2,-2, 2, 2, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12011		new NutationModel( 0, 0, 2, 4, 0, 7.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12012		new NutationModel( 1, 0, 2, 3, 2, 7.0, 0.0, 0.0, -3.0, 0.0, 0.0),
12013		new NutationModel( 4, 0, 0, 2, 0, 4.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12014		new NutationModel( 2, 0, 2, 2, 0, 11.0, 0.0, 0.0, 0.0, 0.0, 0.0),
12015		new NutationModel( 0, 0, 4, 2, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12016		new NutationModel( 4,-1, 2, 0, 2, -6.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12017		new NutationModel( 3, 0, 2, 1, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12018		new NutationModel( 2, 1, 2, 2, 1, 3.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12019		new NutationModel( 4, 1, 2, 0, 2, 5.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12020
12021		/* 671-678 */
12022		new NutationModel(-1,-1, 2, 6, 2, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12023		new NutationModel(-1, 0, 2, 6, 1, -4.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12024		new NutationModel( 1,-1, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0),
12025		new NutationModel( 1, 1, 2, 4, 2, 4.0, 0.0, 0.0, -2.0, 0.0, 0.0),
12026		new NutationModel( 3, 1, 2, 2, 2, 3.0, 0.0, 0.0, -1.0, 0.0, 0.0),
12027		new NutationModel( 5, 0, 2, 0, 1, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
12028		new NutationModel( 2,-1, 2, 4, 2, -3.0, 0.0, 0.0, 1.0, 0.0, 0.0),
12029		new NutationModel( 2, 0, 2, 4, 1, -3.0, 0.0, 0.0, 2.0, 0.0, 0.0)
12030		};
12031
12032		/* Number of terms in the luni-solar nutation model */
12033	68	final int NLS = xls.length;
12034
12035		/* ------------------------ */
12036		/* Planetary nutation model */
12037		/* ------------------------ */
12038
12039		/* The units for the sine and cosine coefficients are */
12040		/* 0.1 microarcsecond */
12041
12042		final class PlanetaryNutModel {
12043		final int nl, /* coefficients of l, F, D and Omega */
12044		nf,
12045		nd,
12046		nom,
12047		nme, /* coefficients of planetary longitudes */
12048		nve,
12049		nea,
12050		nma,
12051		nju,
12052		nsa,
12053		nur,
12054		nne,
12055		npa; /* coefficient of general precession */
12056		final int sp,cp; /* longitude sin, cos coefficients */
12057		final int se,ce; /* obliquity sin, cos coefficients */
12058		public PlanetaryNutModel( int nl,
12059		int nf,
12060		int nd,
12061		int nom,
12062		int nme,
12063		int nve,
12064		int nea,
12065		int nma,
12066		int nju,
12067		int nsa,
12068		int nur,
12069		int nne,
12070		int npa,
12071		int sp,int cp,
12072		int se,int ce
12073	46716	) {
12074	46716	this.nl = nl; /* coefficients of l, F, D and Omega */
12075	46716	this.nf = nf;
12076	46716	this.nd = nd;
12077	46716	this.nom = nom;
12078	46716	this.nme = nme; /* coefficients of planetary longitudes */
12079	46716	this.nve = nve;
12080	46716	this.nea = nea;
12081	46716	this.nma = nma;
12082	46716	this.nju = nju;
12083	46716	this.nsa = nsa;
12084	46716	this.nur = nur;
12085	46716	this.nne = nne;
12086	46716	this.npa = npa; /* coefficient of general precession */
12087	46716	this.sp = sp; this.cp = cp; /* longitude sin, cos coefficients */
12088	46716	this.se = se; this.ce = ce; /* obliquity sin, cos coefficients */
12089
12090	46716	}
12091		}
12092
12093	68	PlanetaryNutModel xpl[] = {
12094
12095		/* 1-10 */
12096		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0, 1440, 0, 0, 0),
12097		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -8, 16,-4,-5, 0, 0, 2, 56,-117, -42, -40),
12098		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2, 125, -43, 0, -54),
12099		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 2, 2, 0, 5, 0, 0),
12100		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 8,-1,-5, 0, 0, 2, 3, -7, -3, 0),
12101		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1, 3, 0, 0, -2),
12102		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0, -114, 0, 0, 61),
12103		new PlanetaryNutModel(-1, 0, 0, 0, 0, 10, -3, 0, 0, 0, 0, 0, 0, -219, 89, 0, 0),
12104		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-2, 6,-3, 0, 2, -3, 0, 0, 0),
12105		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, -462,1604, 0, 0),
12106
12107		/* 11-20 */
12108		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -5, 8,-3, 0, 0, 0, 0, 99, 0, 0, -53),
12109		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 8,-3, 0, 0, 0, 1, -3, 0, 0, 2),
12110		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2, 0, 6, 2, 0),
12111		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 6, 4, 0, 0, 0, 0, 2, 3, 0, 0, 0),
12112		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 2, -12, 0, 0, 0),
12113		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 1, 14,-218, 117, 8),
12114		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 2,-5, 0, 0, 0, 31,-481, -257, -17),
12115		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-5, 0, 0, 0, -491, 128, 0, 0),
12116		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-2, 5, 0, 0, 0,-3084,5123, 2735,1647),
12117		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 1,-1444,2409,-1286,-771),
12118
12119		/* 21-30 */
12120		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-2, 5, 0, 0, 2, 11, -24, -11, -9),
12121		new PlanetaryNutModel( 2,-1,-1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, 26, -9, 0, 0),
12122		new PlanetaryNutModel( 1, 0,-2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0, 103, -60, 0, 0),
12123		new PlanetaryNutModel( 0, 1,-1, 1, 0, 2, -4, 0,-3, 0, 0, 0, 0, 0, -13, -7, 0),
12124		new PlanetaryNutModel( 1, 0,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -26, -29, -16, 14),
12125		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-4,10, 0, 0, 0, 9, -27, -14, -5),
12126		new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0, 0,-5, 0, 0, 0, 12, 0, 0, -6),
12127		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0, -7, 0, 0, 0),
12128		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 1,-1, 0, 0, 0, 0, 24, 0, 0),
12129		new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, 284, 0, 0,-151),
12130
12131		/* 31-40 */
12132		new PlanetaryNutModel(-1, 0, 0, 0, 0, 18,-16, 0, 0, 0, 0, 0, 0, 226, 101, 0, 0),
12133		new PlanetaryNutModel(-2, 1, 1, 2, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -8, -2, 0),
12134		new PlanetaryNutModel(-1, 1,-1, 1, 0, 18,-17, 0, 0, 0, 0, 0, 0, 0, -6, -3, 0),
12135		new PlanetaryNutModel(-1, 0, 1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -3),
12136		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 2, -41, 175, 76, 17),
12137		new PlanetaryNutModel( 0, 2,-2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 15, 6, 0),
12138		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 13, 0, 0, 0, 0, 0, 1, 425, 212, -133, 269),
12139		new PlanetaryNutModel( 0, 1,-1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0, 1200, 598, 319,-641),
12140		new PlanetaryNutModel( 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0, 235, 334, 0, 0),
12141		new PlanetaryNutModel( 0, 1,-1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0, 11, -12, -7, -6),
12142
12143		/* 41-50 */
12144		new PlanetaryNutModel( 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1, 5, -6, 3, 3),
12145		new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-4, 5, 0, 0, 0, -5, 0, 0, 3),
12146		new PlanetaryNutModel(-2, 0, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3),
12147		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-3, 1, 0, 0, 0, 15, 0, 0, 0),
12148		new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0, 13, 0, 0, -7),
12149		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-4, 3, 0, 0, 0, -6, -9, 0, 0),
12150		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 266, -78, 0, 0),
12151		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0, -460,-435, -232, 246),
12152		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0, 15, 7, 0),
12153		new PlanetaryNutModel(-1, 1, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12154
12155		/* 51-60 */
12156		new PlanetaryNutModel(-1, 0, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 131, 0, 0),
12157		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-2,-2, 0, 0, 0, 4, 0, 0, 0),
12158		new PlanetaryNutModel(-2, 2, 0, 2, 0, 0, -5, 9, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12159		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 0,-1, 0, 0, 0, 4, 2, 0),
12160		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0),
12161		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, -17, -19, -10, 9),
12162		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, -9, -11, 6, -5),
12163		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, -6, 0, 0, 3),
12164		new PlanetaryNutModel(-1, 0, 1, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -16, 8, 0, 0),
12165		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0),
12166
12167		/* 61-70 */
12168		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0, 11, 24, 11, -5),
12169		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0, -3, -4, -2, 1),
12170		new PlanetaryNutModel( 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12171		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-1, 2, 0, 0, 0, 0, -8, -4, 0),
12172		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1,-2, 0, 0, 0, 0, 3, 0, 0),
12173		new PlanetaryNutModel( 1, 0,-2, 0, 0, 17,-16, 0,-2, 0, 0, 0, 0, 0, 5, 0, 0),
12174		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 1,-3, 0, 0, 0, 0, 3, 2, 0),
12175		new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 5, -6, 0, 0, 0, 0, 0, -6, 4, 2, 3),
12176		new PlanetaryNutModel( 0,-2, 2, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, -3, -5, 0, 0),
12177		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0, -5, 0, 0, 2),
12178
12179		/* 71-80 */
12180		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 4, 24, 13, -2),
12181		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, -42, 20, 0, 0),
12182		new PlanetaryNutModel( 0,-2, 2, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, -10, 233, 0, 0),
12183		new PlanetaryNutModel( 0,-1, 1, 1, 0, 5, -7, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12184		new PlanetaryNutModel(-2, 0, 2, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 78, -18, 0, 0),
12185		new PlanetaryNutModel( 2, 1,-3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12186		new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -3, -1, 0),
12187		new PlanetaryNutModel( 0,-1, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, -4, -2, 1),
12188		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, -8, -4, -1),
12189		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, -5, 3, 0),
12190
12191		/* 81-90 */
12192		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -7, 0, 0, 3),
12193		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 2, -14, 8, 3, 6),
12194		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 1, 0, 8, -4, 0),
12195		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0, 0, 19, 10, 0),
12196		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, 45, -22, 0, 0),
12197		new PlanetaryNutModel( 1,-1,-1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12198		new PlanetaryNutModel( 2, 0,-2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12199		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-5, 5, 0, 0, 0, 0, 3, 0, 0),
12200		new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0, 3, 5, 3, -2),
12201		new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 89, -16, -9, -48),
12202
12203		/* 91-100 */
12204		new PlanetaryNutModel(-2, 1, 1, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, 0, 3, 0, 0),
12205		new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, 1, 0,-3, 0, 0, 0, 0, -3, 7, 4, 2),
12206		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -349, -62, 0, 0),
12207		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -15, 22, 0, 0),
12208		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-1,-5, 0, 0, 0, -3, 0, 0, 0),
12209		new PlanetaryNutModel(-1, 0, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, -53, 0, 0, 0),
12210		new PlanetaryNutModel(-1, 1, 1, 1, 0,-20, 20, 0, 0, 0, 0, 0, 0, 5, 0, 0, -3),
12211		new PlanetaryNutModel( 1, 0,-2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0),
12212		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0, 15, -7, -4, -8),
12213		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12214
12215		/* 101-110 */
12216		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -21, -78, 0, 0),
12217		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 20, -70, -37, -11),
12218		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, 6, 3, 0),
12219		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-2, 4, 0, 0, 0, 5, 3, 2, -2),
12220		new PlanetaryNutModel( 2, 0,-2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0, -17, -4, -2, 9),
12221		new PlanetaryNutModel( 0,-2, 2, 1, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0),
12222		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 1, 32, 15, -8, 17),
12223		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0,-1, 0, 0, 0, 174, 84, 45, -93),
12224		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 11, 56, 0, 0),
12225		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0, -66, -12, -6, 35),
12226
12227		/* 111-120 */
12228		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 47, 8, 4, -25),
12229		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 8, 4, 0),
12230		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0, 10, -22, -12, -5),
12231		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 7,-13, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12232		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -24, 12, 0, 0),
12233		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, 0, 5, -6, 0, 0),
12234		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -9, 17, 0, 0, 0, 0, 2, 3, 0, 0, -2),
12235		new PlanetaryNutModel( 1, 0,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 4, 3, 1, -2),
12236		new PlanetaryNutModel( 1, 0,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 29, 15, 0),
12237		new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0, -5, -4, -2, 2),
12238
12239		/* 121-130 */
12240		new PlanetaryNutModel( 0,-1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 8, -3, -1, -5),
12241		new PlanetaryNutModel( 0,-2, 2, 0, 1, 0, -2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12242		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0, 10, 0, 0, 0),
12243		new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-3, 1, 0, 0, 0, 3, 0, 0, -2),
12244		new PlanetaryNutModel(-2, 0, 2, 1, 0, 3, -3, 0, 0, 0, 0, 0, 0, -5, 0, 0, 3),
12245		new PlanetaryNutModel( 0, 0, 0, 1, 0, 8,-13, 0, 0, 0, 0, 0, 0, 46, 66, 35, -25),
12246		new PlanetaryNutModel( 0,-1, 1, 0, 0, 8,-12, 0, 0, 0, 0, 0, 0, -14, 7, 0, 0),
12247		new PlanetaryNutModel( 0, 2,-2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0),
12248		new PlanetaryNutModel(-1, 0, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12249		new PlanetaryNutModel(-1, 0, 0, 1, 0, 18,-16, 0, 0, 0, 0, 0, 0, -68, -34, -18, 36),
12250
12251		/* 131-140 */
12252		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-1, 1, 0, 0, 0, 0, 14, 7, 0),
12253		new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0, 10, -6, -3, -5),
12254		new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, -3, 7, 0, 0, 0, 0, 0, -5, -4, -2, 3),
12255		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0,-2, 5, 0, 0, 0, -3, 5, 2, 1),
12256		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0,-2, 5, 0, 0, 0, 76, 17, 9, -41),
12257		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 84, 298, 159, -45),
12258		new PlanetaryNutModel( 1, 0, 0, 1, 0,-10, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12259		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12260		new PlanetaryNutModel(-1, 0, 0, 1, 0, 10, -3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12261		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, -82, 292, 156, 44),
12262
12263		/* 141-150 */
12264		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 2,-5, 0, 0, 0, -73, 17, 9, 39),
12265		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -9, -16, 0, 0),
12266		new PlanetaryNutModel( 2,-1,-1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0, 3, 0, -1, -2),
12267		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0, 0,-5, 0, 0, 0, -3, 0, 0, 0),
12268		new PlanetaryNutModel( 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0, -9, -5, -3, 5),
12269		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -439, 0, 0, 0),
12270		new PlanetaryNutModel( 1, 0, 0, 1, 0,-18, 16, 0, 0, 0, 0, 0, 0, 57, -28, -15, -30),
12271		new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -6, -3, 0),
12272		new PlanetaryNutModel( 0, 1,-1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2),
12273		new PlanetaryNutModel( 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0, -40, 57, 30, 21),
12274
12275		/* 151-160 */
12276		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1, 23, 7, 3, -13),
12277		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 273, 80, 43,-146),
12278		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -449, 430, 0, 0),
12279		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, -8, -47, -25, 4),
12280		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 1, 6, 47, 25, -3),
12281		new PlanetaryNutModel(-1, 0, 1, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, 23, 13, 0),
12282		new PlanetaryNutModel(-1, 0, 1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, -3, 0, 0, 2),
12283		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0,-2, 0, 0, 0, 3, -4, -2, -2),
12284		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0, -48,-110, -59, 26),
12285		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 51, 114, 61, -27),
12286
12287		/* 161-170 */
12288		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, -133, 0, 0, 57),
12289		new PlanetaryNutModel( 0, 1,-1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0),
12290		new PlanetaryNutModel( 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0, -21, -6, -3, 11),
12291		new PlanetaryNutModel( 0, 1,-1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, -3, -1, 0),
12292		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0, -11, -21, -11, 6),
12293		new PlanetaryNutModel( 0, 2,-2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, -18,-436, -233, 9),
12294		new PlanetaryNutModel( 0,-1, 1, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 35, -7, 0, 0),
12295		new PlanetaryNutModel( 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12296		new PlanetaryNutModel(-2, 0, 2, 1, 0, 6, -8, 0, 0, 0, 0, 0, 0, 11, -3, -1, -6),
12297		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0, -5, -3, -1, 3),
12298
12299		/* 171-180 */
12300		new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 2, 0,-3, 0, 0, 0, 0, -53, -9, -5, 28),
12301		new PlanetaryNutModel(-2, 0, 2, 1, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, 3, 2, 1),
12302		new PlanetaryNutModel( 1, 0,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 4, 0, 0, -2),
12303		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3,-5, 0, 0, 0, 0, -4, 0, 0),
12304		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0,-1, 0, 0, 0, 0, -50, 194, 103, 27),
12305		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0,-1, 0, 0, 0, 1, -13, 52, 28, 7),
12306		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, -91, 248, 0, 0),
12307		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 6, 49, 26, -3),
12308		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, -6, -47, -25, 3),
12309		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 5, 3, 0),
12310
12311		/* 181-190 */
12312		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 52, 23, 10, -23),
12313		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 0,-1, 0, 0, 0, -3, 0, 0, 1),
12314		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0, 0,-1, 0, 0, 0, 0, 5, 3, 0),
12315		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -4, 0, 0, 0),
12316		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -7, 13, 0, 0, 0, 0, 2, -4, 8, 3, 2),
12317		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, 0, 10, 0, 0, 0),
12318		new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12319		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0, 0, 8, 4, 0),
12320		new PlanetaryNutModel( 0, 2,-2, 1,-1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 8, 4, 1),
12321		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12322
12323		/* 191-200 */
12324		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, -4, 0, 0, 0),
12325		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0, -8, 4, 2, 4),
12326		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 8, -4, -2, -4),
12327		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 15, 7, 0),
12328		new PlanetaryNutModel(-2, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -138, 0, 0, 0),
12329		new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, -7, -3, 0),
12330		new PlanetaryNutModel( 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -7, -3, 0),
12331		new PlanetaryNutModel( 2, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 54, 0, 0, -29),
12332		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 10, 4, 0),
12333		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0, -7, 0, 0, 3),
12334
12335		/* 201-210 */
12336		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0, -37, 35, 19, 20),
12337		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0),
12338		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -4, 9, 0, 0),
12339		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0, 8, 0, 0, -4),
12340		new PlanetaryNutModel( 0, 1,-1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0, -9, -14, -8, 5),
12341		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1, -3, -9, -5, 3),
12342		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0, -145, 47, 0, 0),
12343		new PlanetaryNutModel( 0, 1,-1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, -10, 40, 21, 5),
12344		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 1, 11, -49, -26, -7),
12345		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2,-2150, 0, 0, 932),
12346
12347		/* 211-220 */
12348		new PlanetaryNutModel( 0, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -12, 0, 0, 5),
12349		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 0, 2, 85, 0, 0, -37),
12350		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1, 4, 0, 0, -2),
12351		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12352		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -86, 153, 0, 0),
12353		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -6, 9, 5, 3),
12354		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 9, -13, -7, -5),
12355		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 1, -8, 12, 6, 4),
12356		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 2, -51, 0, 0, 22),
12357		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, -11,-268, -116, 5),
12358
12359		/* 221-230 */
12360		new PlanetaryNutModel( 0, 2,-2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 12, 5, 0),
12361		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 2, 0, 7, 3, 0),
12362		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 31, 6, 3, -17),
12363		new PlanetaryNutModel( 0, 1,-1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0, 140, 27, 14, -75),
12364		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 0, 1, 57, 11, 6, -30),
12365		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, -14, -39, 0, 0),
12366		new PlanetaryNutModel( 0, 1,-1, 2, 0, 0, -1, 0,-1, 0, 0, 0, 0, 0, -6, -2, 0),
12367		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 0, 0,-1, 0, 0, 0, 0, 4, 15, 8, -2),
12368		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 0, 4, 0, 0),
12369		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0, -3, 0, 0, 1),
12370
12371		/* 231-240 */
12372		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 11, 0, 0, 0, 0, 2, 0, 11, 5, 0),
12373		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, 0, 9, 6, 0, 0),
12374		new PlanetaryNutModel( 0, 0, 0, 0,-1, 0, 4, 0, 0, 0, 0, 0, 2, -4, 10, 4, 2),
12375		new PlanetaryNutModel( 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0, 5, 3, 0, 0),
12376		new PlanetaryNutModel( 2, 0,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 16, 0, 0, -9),
12377		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, -3, 0, 0, 0),
12378		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0, 0, 3, 2, -1),
12379		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 4,-5, 0, 0, 2, 7, 0, 0, -3),
12380		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -25, 22, 0, 0),
12381		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 42, 223, 119, -22),
12382
12383		/* 241-250 */
12384		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, -27,-143, -77, 14),
12385		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 9, 49, 26, -5),
12386		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2,-1166, 0, 0, 505),
12387		new PlanetaryNutModel( 0, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -5, 0, 0, 2),
12388		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2, -6, 0, 0, 3),
12389		new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0, -8, 0, 1, 4),
12390		new PlanetaryNutModel( 0,-1, 1, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12391		new PlanetaryNutModel( 0, 2,-2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0, 117, 0, 0, -63),
12392		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0, -4, 8, 4, 2),
12393		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12394
12395		/* 251-260 */
12396		new PlanetaryNutModel( 0, 1,-1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0, -5, 0, 0, 2),
12397		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 31, 0, 0),
12398		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -5, 0, 1, 3),
12399		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0, 4, 0, 0, -2),
12400		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12401		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 2, -24, -13, -6, 10),
12402		new PlanetaryNutModel( 0,-1, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0),
12403		new PlanetaryNutModel( 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, -32, -17, 0),
12404		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 2, 8, 12, 5, -3),
12405		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 1, 3, 0, 0, -1),
12406
12407		/* 261-270 */
12408		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, 7, 13, 0, 0),
12409		new PlanetaryNutModel( 0,-1, 1, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -3, 16, 0, 0),
12410		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 50, 0, 0, -27),
12411		new PlanetaryNutModel(-2, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -5, -3, 0),
12412		new PlanetaryNutModel( 0,-2, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0),
12413		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 1, 0, 5, 3, 1),
12414		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 2, 24, 5, 2, -11),
12415		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 2, 5, -11, -5, -2),
12416		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 3, 0, 0, 0, 0, 0, 1, 30, -3, -2, -16),
12417		new PlanetaryNutModel( 0, 1,-1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 18, 0, 0, -9),
12418
12419		/* 271-280 */
12420		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0, 8, 614, 0, 0),
12421		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1, 3, -3, -1, -2),
12422		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 6, 17, 9, -3),
12423		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0, -3, -9, -5, 2),
12424		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 6, 3, -1),
12425		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, -127, 21, 9, 55),
12426		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, 3, 5, 0, 0),
12427		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 2, -6, -10, -4, 3),
12428		new PlanetaryNutModel( 0,-2, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 5, 0, 0, 0),
12429		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 2, 16, 9, 4, -7),
12430
12431		/* 281-290 */
12432		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 1, 3, 0, 0, -2),
12433		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, 0, 22, 0, 0),
12434		new PlanetaryNutModel( 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 19, 10, 0),
12435		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 7, 0, 0, -4),
12436		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 2, 0, -5, -2, 0),
12437		new PlanetaryNutModel( 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12438		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2, -9, 3, 1, 4),
12439		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 2, 17, 0, 0, -7),
12440		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 5, 0, 0, 0, 0, 1, 0, -3, -2, -1),
12441		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -20, 34, 0, 0),
12442
12443		/* 291-300 */
12444		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1, -10, 0, 1, 5),
12445		new PlanetaryNutModel( 0, 1,-1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0, -4, 0, 0, 2),
12446		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 22, -87, 0, 0),
12447		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12448		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 2, 0, 0, 0, 0, 0, 2, -3, -6, -2, 1),
12449		new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 2, -16, -3, -1, 7),
12450		new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 11, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0),
12451		new PlanetaryNutModel( 0,-2, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0),
12452		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -68, 39, 0, 0),
12453		new PlanetaryNutModel( 0, 2,-2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0, 27, 0, 0, -14),
12454
12455		/* 301-310 */
12456		new PlanetaryNutModel( 0,-1, 1, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12457		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -25, 0, 0, 0),
12458		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 1, -12, -3, -2, 6),
12459		new PlanetaryNutModel( 0, 1,-1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12460		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 7, 0, 0, 0, 0, 0, 2, 3, 66, 29, -1),
12461		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 2, 490, 0, 0,-213),
12462		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -22, 93, 49, 12),
12463		new PlanetaryNutModel( 0, 1,-1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0, -7, 28, 15, 4),
12464		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 0, 1, -3, 13, 7, 2),
12465		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0, -46, 14, 0, 0),
12466
12467		/* 311-320 */
12468		new PlanetaryNutModel(-2, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12469		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0),
12470		new PlanetaryNutModel( 0,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12471		new PlanetaryNutModel( 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, -28, 0, 0, 15),
12472		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2),
12473		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12474		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 2, -11, 0, 0, 5),
12475		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -7, 12, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12476		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12477		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 1, 25, 106, 57, -13),
12478
12479		/* 321-330 */
12480		new PlanetaryNutModel( 0, 1,-1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 21, 11, -3),
12481		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, 1485, 0, 0, 0),
12482		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1, -7, -32, -17, 4),
12483		new PlanetaryNutModel( 0, 1,-1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12484		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 2, -6, -3, -2, 3),
12485		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 4, 0, 0, 0, 2, 30, -6, -2, -13),
12486		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-4, 0, 0, 0, 0, -4, 4, 0, 0),
12487		new PlanetaryNutModel( 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0, -19, 0, 0, 10),
12488		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 2, 0, 4, 2, -1),
12489		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 10, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12490
12491		/* 331-340 */
12492		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0, 4, 0, 0, -2),
12493		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 2, 0, -3, -1, 0),
12494		new PlanetaryNutModel(-2, 0, 2, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12495		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 8, 0, 0, 0, 0, 2, 5, 3, 1, -2),
12496		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0, 11, 0, 0),
12497		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 2, 118, 0, 0, -52),
12498		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 3, 0, 0, 0, 1, 0, -5, -3, 0),
12499		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-3, 0, 0, 0, 0, -28, 36, 0, 0),
12500		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0),
12501		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 1, 14, -59, -31, -8),
12502
12503		/* 341-350 */
12504		new PlanetaryNutModel( 0, 1,-1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 9, 5, 1),
12505		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 4, 0, 0, 0, 0, 0, 2, -458, 0, 0, 198),
12506		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 2, 0, -45, -20, 0),
12507		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 0, 1, 9, 0, 0, -5),
12508		new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12509		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 1, 0,-2, 0, 0, 0, 0, 0, -4, -2, -1),
12510		new PlanetaryNutModel( 0, 2,-2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 11, 0, 0, -6),
12511		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -4, 6, 0, 0, 0, 0, 2, 6, 0, 0, -2),
12512		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -16, 23, 0, 0),
12513		new PlanetaryNutModel( 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0, 0, -4, -2, 0),
12514
12515		/* 351-360 */
12516		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 2, 0, 0, 0, 2, -5, 0, 0, 2),
12517		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-2, 0, 0, 0, 0, -166, 269, 0, 0),
12518		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, 15, 0, 0, -8),
12519		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 9, 0, 0, 0, 0, 0, 2, 10, 0, 0, -4),
12520		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -78, 45, 0, 0),
12521		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 2, 0, -5, -2, 0),
12522		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0, 1, 7, 0, 0, -4),
12523		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0, -5, 328, 0, 0),
12524		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2),
12525		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0, 5, 0, 0, -2),
12526
12527		/* 361-370 */
12528		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, 3, 1, 0),
12529		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0,-3, 0, 0, 0, -3, 0, 0, 0),
12530		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1,-5, 0, 0, 0, -3, 0, 0, 0),
12531		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 1, 0, -4, -2, 0),
12532		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0,-1223, -26, 0, 0),
12533		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 1, 0, 7, 3, 0),
12534		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-3, 5, 0, 0, 0, 3, 0, 0, 0),
12535		new PlanetaryNutModel( 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0),
12536		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0,-2, 0, 0, 0, -6, 20, 0, 0),
12537		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -368, 0, 0, 0),
12538
12539		/* 371-380 */
12540		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0,-1, 0, 0, 0, -75, 0, 0, 0),
12541		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 11, 0, 0, -6),
12542		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 3, 0, 0, -2),
12543		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 14, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12544		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 2,-5, 0, 0, 0, -13, -30, 0, 0),
12545		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0, 21, 3, 0, 0),
12546		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2, -3, 0, 0, 1),
12547		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12548		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 8, -27, 0, 0),
12549		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0, -19, -11, 0, 0),
12550
12551		/* 381-390 */
12552		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 8,-3, 0, 0, 0, 2, -4, 0, 0, 2),
12553		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0,-2, 5, 0, 0, 2, 0, 5, 2, 0),
12554		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 2, -6, 0, 0, 2),
12555		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0),
12556		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1,-2, 0, 0, 0, -1, 0, 0, 0),
12557		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, -14, 0, 0, 6),
12558		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 6, 0, 0, 0),
12559		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, -74, 0, 0, 32),
12560		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, -3, -1, 0),
12561		new PlanetaryNutModel( 0, 2,-2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2),
12562
12563		/* 391-400 */
12564		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 8, 11, 0, 0),
12565		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 3, 2, 0),
12566		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, -262, 0, 0, 114),
12567		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12568		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 1, -7, 0, 0, 4),
12569		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 6, 0, 0, 0, 0, 0, 2, 0, -27, -12, 0),
12570		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 2, -19, -8, -4, 8),
12571		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 2, 202, 0, 0, -87),
12572		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 0, 1, -8, 35, 19, 5),
12573		new PlanetaryNutModel( 0, 1,-1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0),
12574
12575		/* 401-410 */
12576		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0, 16, -5, 0, 0),
12577		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0, 5, 0, 0, -3),
12578		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0, 0, -3, 0, 0),
12579		new PlanetaryNutModel( 0, 0, 0, 0,-1, 0, 3, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0),
12580		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, -35, -48, -21, 15),
12581		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 2, -3, -5, -2, 1),
12582		new PlanetaryNutModel( 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, -3),
12583		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 9, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12584		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0, -5, 0, 0),
12585		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0, 1, 12, 55, 29, -6),
12586
12587		/* 411-420 */
12588		new PlanetaryNutModel( 0, 1,-1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12589		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, -598, 0, 0, 0),
12590		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1, -3, -13, -7, 1),
12591		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2, -5, -7, -3, 2),
12592		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 7, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12593		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 5, -7, 0, 0),
12594		new PlanetaryNutModel( 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2),
12595		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 16, -6, 0, 0),
12596		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0, 8, -3, 0, 0),
12597		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 1, 8, -31, -16, -4),
12598
12599		/* 421-430 */
12600		new PlanetaryNutModel( 0, 1,-1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12601		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 3, 0, 0, 0, 0, 0, 2, 113, 0, 0, -49),
12602		new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 2, 0, -24, -10, 0),
12603		new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 10, 0, 0, 0, 0, 0, 1, 4, 0, 0, -2),
12604		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 27, 0, 0, 0),
12605		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 8, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12606		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 2, 0, -4, -2, 0),
12607		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 5, 0, 0, 0, 0, 0, 1, 5, 0, 0, -2),
12608		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0),
12609		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, -13, 0, 0, 6),
12610
12611		/* 431-440 */
12612		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 0, 5, 0, 0, 0, 2, 5, 0, 0, -2),
12613		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2, -18, -10, -4, 8),
12614		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, -28, 0, 0),
12615		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, -5, 6, 3, 2),
12616		new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12617		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 5, 0, 0, 0, 0, 2, -5, -9, -4, 2),
12618		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 0, 4, 0, 0, 0, 2, 17, 0, 0, -7),
12619		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-4, 0, 0, 0, 0, 11, 4, 0, 0),
12620		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 7, 0, 0, 0, 0, 2, 0, -6, -2, 0),
12621		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 83, 15, 0, 0),
12622
12623		/* 441-450 */
12624		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 1, -4, 0, 0, 2),
12625		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 5, 0, 0, 0, 0, 0, 2, 0,-114, -49, 0),
12626		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 2, 117, 0, 0, -51),
12627		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0, 1, -5, 19, 10, 2),
12628		new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12629		new PlanetaryNutModel( 0, 0, 0, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2),
12630		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 9, 0, 0, 0, 0, 2, 0, -3, -1, 0),
12631		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 3, 0, 0, 0),
12632		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2, 0, -6, -2, 0),
12633		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 393, 3, 0, 0),
12634
12635		/* 451-460 */
12636		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 1, -4, 21, 11, 2),
12637		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 2, -6, 0, -1, 3),
12638		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 10, 0, 0, 0, 0, 0, 2, -3, 8, 4, 1),
12639		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 8, 0, 0, 0),
12640		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2, 18, -29, -13, -8),
12641		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 1, 8, 34, 18, -4),
12642		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 89, 0, 0, 0),
12643		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1, 3, 12, 6, -1),
12644		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2, 54, -15, -7, -24),
12645		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-3, 0, 0, 0, 0, 3, 0, 0),
12646
12647		/* 461-470 */
12648		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 13, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12649		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 0, 0, 35, 0, 0),
12650		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-1, 0, 0, 0, 2, -154, -30, -13, 67),
12651		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 0, 15, 0, 0, 0),
12652		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-2, 0, 0, 1, 0, 4, 2, 0),
12653		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 9, 0, 0),
12654		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2, 80, -71, -31, -35),
12655		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0,-1, 0, 0, 2, 0, -20, -9, 0),
12656		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 15, 0, 0, 0, 0, 2, 11, 5, 2, -5),
12657		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 15, 0, 0, 0, 0, 0, 2, 61, -96, -42, -27),
12658
12659		/* 471-480 */
12660		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 9, -4, 0, 0, 0, 0, 2, 14, 9, 4, -6),
12661		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 2,-5, 0, 0, 2, -11, -6, -3, 5),
12662		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 8,-1,-5, 0, 0, 2, 0, -3, -1, 0),
12663		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2, 123,-415, -180, -53),
12664		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, -35),
12665		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12666		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 7, -32, -17, -4),
12667		new PlanetaryNutModel( 0, 1,-1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -9, -5, 0),
12668		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, -4, 2, 0),
12669		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, -89, 0, 0, 38),
12670
12671		/* 481-490 */
12672		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -6, 16,-4,-5, 0, 0, 2, 0, -86, -19, -6),
12673		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, 0, 0, -19, 6),
12674		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -2, 8,-3, 0, 0, 0, 2, -123,-416, -180, 53),
12675		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2, 0, -3, -1, 0),
12676		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 5, 0, 0, 2, 12, -6, -3, -5),
12677		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2, -13, 9, 4, 6),
12678		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, 0, -15, -7, 0),
12679		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1),
12680		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 11, 0, 0, 0, 0, 0, 2, -62, -97, -42, 27),
12681		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2, -11, 5, 2, 5),
12682
12683		/* 491-500 */
12684		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, -19, -8, 0),
12685		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2, -3, 0, 0, 1),
12686		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 4, 2, 0),
12687		new PlanetaryNutModel( 0, 1,-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12688		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 4, 2, 0),
12689		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, -85, -70, -31, 37),
12690		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 163, -12, -5, -72),
12691		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 7, 0, 0, 0, 0, 0, 2, -63, -16, -7, 28),
12692		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2, -21, -32, -14, 9),
12693		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 2, 0, -3, -1, 0),
12694
12695		/* 501-510 */
12696		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0, 1, 3, 0, 0, -2),
12697		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0),
12698		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2, 3, 10, 4, -1),
12699		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2, 3, 0, 0, -1),
12700		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 6, 0, 0, 0, 0, 2, 0, -7, -3, 0),
12701		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2, 0, -4, -2, 0),
12702		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0, 6, 19, 0, 0),
12703		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2, 5,-173, -75, -2),
12704		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2, 0, -7, -3, 0),
12705		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2, 7, -12, -5, -3),
12706
12707		/* 511-520 */
12708		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 1, -3, 0, 0, 2),
12709		new PlanetaryNutModel( 0, 0, 0, 0, 0, -1, 4, 0, 0, 0, 0, 0, 2, 3, -4, -2, -1),
12710		new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 2, 74, 0, 0, -32),
12711		new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 9, 0, 0, 0, 0, 0, 1, -3, 12, 6, 2),
12712		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2, 26, -14, -6, -11),
12713		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2, 19, 0, 0, -8),
12714		new PlanetaryNutModel( 0, 0, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0, 1, 6, 24, 13, -3),
12715		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0, 83, 0, 0, 0),
12716		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1, 0, -10, -5, 0),
12717		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2, 11, -3, -1, -5),
12718
12719		/* 521-530 */
12720		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 3, 0, 1, -1),
12721		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -3, 0, 5, 0, 0, 0, 2, 3, 0, 0, -1),
12722		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12723		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 5, -23, -12, -3),
12724		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, -339, 0, 0, 147),
12725		new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 12, 0, 0, 0, 0, 0, 2, 0, -10, -5, 0),
12726		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-4, 0, 0, 0, 0, 5, 0, 0, 0),
12727		new PlanetaryNutModel( 0, 2,-2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12728		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2, 0, -4, -2, 0),
12729		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 0, 18, -3, 0, 0),
12730
12731		/* 531-540 */
12732		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-3, 0, 0, 0, 2, 9, -11, -5, -4),
12733		new PlanetaryNutModel( 0, 0, 0, 0, 0, -2, 6, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4),
12734		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 7, 0, 0, 0, 0, 0, 1, 3, 0, 0, -1),
12735		new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0),
12736		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2, 6, -9, -4, -2),
12737		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 0, -4, -12, 0, 0),
12738		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-2, 0, 0, 0, 2, 67, -91, -39, -29),
12739		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2, 30, -18, -8, -13),
12740		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0),
12741		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2, 0,-114, -50, 0),
12742
12743		/* 541-550 */
12744		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 0, 0, 0, 23),
12745		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0,-1, 0, 0, 0, 2, 517, 16, 7,-224),
12746		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 0,-2, 0, 0, 2, 0, -7, -3, 0),
12747		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2, 143, -3, -1, -62),
12748		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 0,-1, 0, 0, 2, 29, 0, 0, -13),
12749		new PlanetaryNutModel( 0, 2,-2, 1, 0, 0, 1, 0,-1, 0, 0, 0, 0, -4, 0, 0, 2),
12750		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 16, 0, 0, 0, 0, 0, 2, -6, 0, 0, 3),
12751		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 2,-5, 0, 0, 2, 5, 12, 5, -2),
12752		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2, -25, 0, 0, 11),
12753		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -5, 16,-4,-5, 0, 0, 2, -3, 0, 0, 1),
12754
12755		/* 551-560 */
12756		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0),
12757		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, -1, 8,-3, 0, 0, 0, 2, -22, 12, 5, 10),
12758		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 50, 0, 0, -22),
12759		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0),
12760		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 10, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12761		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2, -4, 4, 2, 2),
12762		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2, -5, -11, -5, 2),
12763		new PlanetaryNutModel( 0, 0, 0, 0, 0, -3, 8, 0, 0, 0, 0, 0, 2, 0, 4, 2, 0),
12764		new PlanetaryNutModel( 0, 0, 0, 0, 0, -5, 5, 0, 0, 0, 0, 0, 1, 4, 17, 9, -2),
12765		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0, 59, 0, 0, 0),
12766
12767		/* 561-570 */
12768		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1, 0, -4, -2, 0),
12769		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2, -8, 0, 0, 4),
12770		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12771		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 4, -15, -8, -2),
12772		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2, 370, -8, 0,-160),
12773		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 0, -3, 0),
12774		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12775		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2, -6, 3, 1, 3),
12776		new PlanetaryNutModel( 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0),
12777		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2, -10, 0, 0, 4),
12778
12779		/* 571-580 */
12780		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2, 0, 9, 4, 0),
12781		new PlanetaryNutModel( 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 4, 17, 7, -2),
12782		new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 2, 34, 0, 0, -15),
12783		new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 11, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0),
12784		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-4, 0, 0, 0, 2, -5, 0, 0, 2),
12785		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-3, 0, 0, 0, 2, -37, -7, -3, 16),
12786		new PlanetaryNutModel( 0, 0, 0, 0, 0, -6, 6, 0, 0, 0, 0, 0, 1, 3, 13, 7, -2),
12787		new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0, 40, 0, 0, 0),
12788		new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0),
12789		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-2, 0, 0, 0, 2, -184, -3, -1, 80),
12790
12791		/* 581-590 */
12792		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2, -3, 0, 0, 1),
12793		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0),
12794		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1, 0, -10, -6, -1),
12795		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2, 31, -6, 0, -13),
12796		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0,-1, 0, 0, 0, 2, -3, -32, -14, 1),
12797		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0, 0,-2, 0, 0, 2, -7, 0, 0, 3),
12798		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2, 0, -8, -4, 0),
12799		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0),
12800		new PlanetaryNutModel( 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0),
12801		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2, 0, 3, 1, 0),
12802
12803		/* 591-600 */
12804		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 19, -23, -10, 2),
12805		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -10),
12806		new PlanetaryNutModel( 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1, 0, 3, 2, 0),
12807		new PlanetaryNutModel( 0, 0, 0, 0, 0, -7, 7, 0, 0, 0, 0, 0, 1, 0, 9, 5, -1),
12808		new PlanetaryNutModel( 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0, 28, 0, 0, 0),
12809		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1, 0, -7, -4, 0),
12810		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2, 8, -4, 0, -4),
12811		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0),
12812		new PlanetaryNutModel( 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12813		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, 0,-4, 0, 0, 0, 2, -3, 0, 0, 1),
12814
12815		/* 601-610 */
12816		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, 0,-3, 0, 0, 0, 2, -9, 0, 1, 4),
12817		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 5, 0,-2, 0, 0, 0, 2, 3, 12, 5, -1),
12818		new PlanetaryNutModel( 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 17, -3, -1, 0),
12819		new PlanetaryNutModel( 0, 0, 0, 0, 0, -8, 8, 0, 0, 0, 0, 0, 1, 0, 7, 4, 0),
12820		new PlanetaryNutModel( 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0, 19, 0, 0, 0),
12821		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1, 0, -5, -3, 0),
12822		new PlanetaryNutModel( 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2, 14, -3, 0, -1),
12823		new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0),
12824		new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 0, 0, -5),
12825		new PlanetaryNutModel( 0, 0, 0, 0, 0, -9, 9, 0, 0, 0, 0, 0, 1, 0, 5, 3, 0),
12826
12827		/* 611-620 */
12828		new PlanetaryNutModel( 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0),
12829		new PlanetaryNutModel( 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1, 0, -3, -2, 0),
12830		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 2, 9, 4, 3),
12831		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4),
12832		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0),
12833		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 4, 2, 0),
12834		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 6, 0, 0, -3),
12835		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0),
12836		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1, 0, 3, 1, 0),
12837		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2, 5, 0, 0, -2),
12838
12839		/* 621-630 */
12840		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, -1),
12841		new PlanetaryNutModel( 1, 0,-2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0),
12842		new PlanetaryNutModel( 1, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0),
12843		new PlanetaryNutModel( 1, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 7, 0, 0, 0),
12844		new PlanetaryNutModel( 1, 0,-2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12845		new PlanetaryNutModel(-1, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0),
12846		new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 6, 0, 0, 0),
12847		new PlanetaryNutModel(-1, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0),
12848		new PlanetaryNutModel( 1, 0,-2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -4, 0, 0),
12849		new PlanetaryNutModel(-2, 0, 2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 5, 0, 0, 0),
12850
12851		/* 631-640 */
12852		new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, -3, 0, 0, 0),
12853		new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0),
12854		new PlanetaryNutModel(-1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -5, 0, 0, 0),
12855		new PlanetaryNutModel(-1, 0, 2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0),
12856		new PlanetaryNutModel( 1,-1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0),
12857		new PlanetaryNutModel(-1, 0, 2, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 13, 0, 0, 0),
12858		new PlanetaryNutModel(-2, 0, 0, 0, 0, 0, 2, 0,-3, 0, 0, 0, 0, 21, 11, 0, 0),
12859		new PlanetaryNutModel( 1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0),
12860		new PlanetaryNutModel(-1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, -5, -2, 0),
12861		new PlanetaryNutModel( 1, 1,-1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 5, 3, 0),
12862
12863		/* 641-650 */
12864		new PlanetaryNutModel(-1, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, -5, 0, 0),
12865		new PlanetaryNutModel(-1, 0, 2, 1, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 2),
12866		new PlanetaryNutModel( 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 20, 10, 0, 0),
12867		new PlanetaryNutModel(-1, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -34, 0, 0, 0),
12868		new PlanetaryNutModel(-1, 0, 2, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0, -19, 0, 0, 0),
12869		new PlanetaryNutModel( 1, 0,-2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0, 3, 0, 0, -2),
12870		new PlanetaryNutModel( 1, 2,-2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12871		new PlanetaryNutModel( 1, 2,-2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0, -6, 0, 0, 3),
12872		new PlanetaryNutModel( 1, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0),
12873		new PlanetaryNutModel( 1, 0, 0, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 3, 0, 0, 0),
12874
12875		/* 651-660 */
12876		new PlanetaryNutModel( 0, 0,-2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0),
12877		new PlanetaryNutModel( 0, 0,-2, 0, 0, 0, 1, 0,-1, 0, 0, 0, 0, 4, 0, 0, 0),
12878		new PlanetaryNutModel( 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12879		new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 6, 0, 0, -3),
12880		new PlanetaryNutModel( 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -8, 0, 0, 3),
12881		new PlanetaryNutModel( 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12882		new PlanetaryNutModel( 0, 0, 2, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 0),
12883		new PlanetaryNutModel( 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -3, -2, 0),
12884		new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 126, -63, -27, -55),
12885		new PlanetaryNutModel(-1, 2, 0, 2, 0, 10, -3, 0, 0, 0, 0, 0, 0, -5, 0, 1, 2),
12886
12887		/* 661-670 */
12888		new PlanetaryNutModel( 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -3, 28, 15, 2),
12889		new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 5, 0, 1, -2),
12890		new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 9, 4, 1),
12891		new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 9, 4, -1),
12892		new PlanetaryNutModel(-1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, -126, -63, -27, 55),
12893		new PlanetaryNutModel( 2, 2,-2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0, 3, 0, 0, -1),
12894		new PlanetaryNutModel( 1, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0, 21, -11, -6, -11),
12895		new PlanetaryNutModel( 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0),
12896		new PlanetaryNutModel(-1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, -21, -11, -6, 11),
12897		new PlanetaryNutModel(-2, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, -3, 0, 0, 1),
12898
12899		/* 671-680 */
12900		new PlanetaryNutModel( 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0),
12901		new PlanetaryNutModel( 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 8, 0, 0, -4),
12902		new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, 1, 0,-1, 0, 0, 0, 0, -6, 0, 0, 3),
12903		new PlanetaryNutModel( 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12904		new PlanetaryNutModel(-1, 2, 2, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0, 3, 0, 0, -1),
12905		new PlanetaryNutModel( 1, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0, -3, 0, 0, 1),
12906		new PlanetaryNutModel(-1, 2, 2, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, -5, 0, 0, 2),
12907		new PlanetaryNutModel( 2, 2, 0, 2, 0, 0, 2, 0,-3, 0, 0, 0, 0, 24, -12, -5, -11),
12908		new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, -4, 8,-3, 0, 0, 0, 0, 0, 3, 1, 0),
12909		new PlanetaryNutModel( 1, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0, 0, 3, 1, 0),
12910
12911		/* 681-687 */
12912		new PlanetaryNutModel( 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0),
12913		new PlanetaryNutModel( 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, -24, -12, -5, 10),
12914		new PlanetaryNutModel( 2, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 4, 0, -1, -2),
12915		new PlanetaryNutModel(-1, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 13, 0, 0, -6),
12916		new PlanetaryNutModel(-1, 2, 2, 2, 0, 3, -3, 0, 0, 0, 0, 0, 0, 7, 0, 0, -3),
12917		new PlanetaryNutModel( 1, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1),
12918		new PlanetaryNutModel( 0, 2, 2, 2, 0, 0, 2, 0,-2, 0, 0, 0, 0, 3, 0, 0, -1)
12919		};
12920
12921		/* Number of terms in the planetary nutation model */
12922	68	final int NPL = xpl.length;
12923
12924		/--------------------------------------------------------------------/
12925
12926		/* Interval between fundamental date J2000.0 and given date (JC). */
12927	68	t = ((date1 - DJ00) + date2) / DJC;
12928
12929		/* ------------------- */
12930		/* LUNI-SOLAR NUTATION */
12931		/* ------------------- */
12932
12933		/* Fundamental (Delaunay) arguments */
12934
12935		/* Mean anomaly of the Moon (IERS 2003). */
12936	68	el = jauFal03(t);
12937
12938		/* Mean anomaly of the Sun (MHB2000). */
12939	68	elp = fmod(1287104.79305 +
12940		t * (129596581.0481 +
12941		t * (-0.5532 +
12942		t * (0.000136 +
12943		t * (-0.00001149)))), TURNAS) * DAS2R;
12944
12945		/* Mean longitude of the Moon minus that of the ascending node */
12946		/* (IERS 2003. */
12947	68	f = jauFaf03(t);
12948
12949		/* Mean elongation of the Moon from the Sun (MHB2000). */
12950	68	d = fmod(1072260.70369 +
12951		t * (1602961601.2090 +
12952		t * (-6.3706 +
12953		t * (0.006593 +
12954		t * (-0.00003169)))), TURNAS) * DAS2R;
12955
12956		/* Mean longitude of the ascending node of the Moon (IERS 2003). */
12957	68	om = jauFaom03(t);
12958
12959		/* Initialize the nutation values. */
12960	68	dp = 0.0;
12961	68	de = 0.0;
12962
12963		/* Summation of luni-solar nutation series (in reverse order). */
12964	46172	for (i = NLS-1; i >= 0; i--) {
12965
12966		/* Argument and functions. */
12967	46104	arg = fmod((double)xls[i].nl * el +
12968		(double)xls[i].nlp * elp +
12969		(double)xls[i].nf * f +
12970		(double)xls[i].nd * d +
12971		(double)xls[i].nom * om, D2PI);
12972	46104	sarg = sin(arg);
12973	46104	carg = cos(arg);
12974
12975		/* Term. */
12976	46104	dp += (xls[i].sp + xls[i].spt * t) * sarg + xls[i].cp * carg;
12977	46104	de += (xls[i].ce + xls[i].cet * t) * carg + xls[i].se * sarg;
12978		}
12979
12980		/* Convert from 0.1 microarcsec units to radians. */
12981	68	dpsils = dp * U2R;
12982	68	depsls = de * U2R;
12983
12984		/* ------------------ */
12985		/* PLANETARY NUTATION */
12986		/* ------------------ */
12987
12988		/* n.b. The MHB2000 code computes the luni-solar and planetary nutation */
12989		/* in different functions, using slightly different Delaunay */
12990		/* arguments in the two cases. This behaviour is faithfully */
12991		/* reproduced here. Use of the IERS 2003 expressions for both */
12992		/* cases leads to negligible changes, well below */
12993		/* 0.1 microarcsecond. */
12994
12995		/* Mean anomaly of the Moon (MHB2000). */
12996	68	al = fmod(2.35555598 + 8328.6914269554 * t, D2PI);
12997
12998		/* Mean longitude of the Moon minus that of the ascending node */
12999		/(MHB2000). /
13000	68	af = fmod(1.627905234 + 8433.466158131 * t, D2PI);
13001
13002		/* Mean elongation of the Moon from the Sun (MHB2000). */
13003	68	ad = fmod(5.198466741 + 7771.3771468121 * t, D2PI);
13004
13005		/* Mean longitude of the ascending node of the Moon (MHB2000). */
13006	68	aom = fmod(2.18243920 - 33.757045 * t, D2PI);
13007
13008		/* General accumulated precession in longitude (IERS 2003). */
13009	68	apa = jauFapa03(t);
13010
13011		/* Planetary longitudes, Mercury through Uranus (IERS 2003). */
13012	68	alme = jauFame03(t);
13013	68	alve = jauFave03(t);
13014	68	alea = jauFae03(t);
13015	68	alma = jauFama03(t);
13016	68	alju = jauFaju03(t);
13017	68	alsa = jauFasa03(t);
13018	68	alur = jauFaur03(t);
13019
13020		/* Neptune longitude (MHB2000). */
13021	68	alne = fmod(5.321159000 + 3.8127774000 * t, D2PI);
13022
13023		/* Initialize the nutation values. */
13024	68	dp = 0.0;
13025	68	de = 0.0;
13026
13027		/* Summation of planetary nutation series (in reverse order). */
13028	46784	for (i = NPL-1; i >= 0; i--) {
13029
13030		/* Argument and functions. */
13031	46716	arg = fmod((double)xpl[i].nl * al +
13032		(double)xpl[i].nf * af +
13033		(double)xpl[i].nd * ad +
13034		(double)xpl[i].nom * aom +
13035		(double)xpl[i].nme * alme +
13036		(double)xpl[i].nve * alve +
13037		(double)xpl[i].nea * alea +
13038		(double)xpl[i].nma * alma +
13039		(double)xpl[i].nju * alju +
13040		(double)xpl[i].nsa * alsa +
13041		(double)xpl[i].nur * alur +
13042		(double)xpl[i].nne * alne +
13043		(double)xpl[i].npa * apa, D2PI);
13044	46716	sarg = sin(arg);
13045	46716	carg = cos(arg);
13046
13047		/* Term. */
13048	46716	dp += (double)xpl[i].sp * sarg + (double)xpl[i].cp * carg;
13049	46716	de += (double)xpl[i].se * sarg + (double)xpl[i].ce * carg;
13050
13051		}
13052
13053		/* Convert from 0.1 microarcsec units to radians. */
13054	68	dpsipl = dp * U2R;
13055	68	depspl = de * U2R;
13056
13057		/* ------- */
13058		/* RESULTS */
13059		/* ------- */
13060
13061		/* Add luni-solar and planetary components. */
13062	68	return new NutationTerms( dpsils + dpsipl,
13063		depsls + depspl);
13064		}
13065
13066
13067		/**
13068		* Nutation, IAU 2000B model.
13069		*
13070		*<p>This function is derived from the International Astronomical Union's
13071		* SOFA (Standards Of Fundamental Astronomy) software collection.
13072		*
13073		*<p>Status: canonical model.
13074		*
13075		*<!-- Given: -->
13076		* @param date1 double TT as a 2-part Julian Date (Note 1)
13077		* @param date2 double TT as a 2-part Julian Date (Note 1)
13078		*
13079		*<!-- Returned: -->
13080		* @return nutation, luni-solar + planetary (Note 2)
13081		*
13082		* <p>Notes:
13083		* <ol>
13084		*
13085		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
13086		* convenient way between the two arguments. For example,
13087		* JD(TT)=2450123.7 could be expressed in any of these ways,
13088		* among others:
13089		*<pre>
13090		* date1 date2
13091		*
13092		* 2450123.7 0.0 (JD method)
13093		* 2451545.0 -1421.3 (J2000 method)
13094		* 2400000.5 50123.2 (MJD method)
13095		* 2450123.5 0.2 (date & time method)
13096		*</pre>
13097		* The JD method is the most natural and convenient to use in
13098		* cases where the loss of several decimal digits of resolution
13099		* is acceptable. The J2000 method is best matched to the way
13100		* the argument is handled internally and will deliver the
13101		* optimum resolution. The MJD method and the date & time methods
13102		* are both good compromises between resolution and convenience.
13103		*
13104		* <li> The nutation components in longitude and obliquity are in radians
13105		* and with respect to the equinox and ecliptic of date. The
13106		* obliquity at J2000.0 is assumed to be the Lieske et al. (1977)
13107		* value of 84381.448 arcsec. (The errors that result from using
13108		* this function with the IAU 2006 value of 84381.406 arcsec can be
13109		* neglected.)
13110		*
13111		* The nutation model consists only of luni-solar terms, but
13112		* includes also a fixed offset which compensates for certain long-
13113		* period planetary terms (Note 7).
13114		*
13115		* <li> This function is an implementation of the IAU 2000B abridged
13116		* nutation model formally adopted by the IAU General Assembly in
13117		* 2000. The function computes the MHB_2000_SHORT luni-solar
13118		* nutation series (Luzum 2001), but without the associated
13119		* corrections for the precession rate adjustments and the offset
13120		* between the GCRS and J2000.0 mean poles.
13121		*
13122		* <li> The full IAU 2000A (MHB2000) nutation model contains nearly 1400
13123		* terms. The IAU 2000B model (McCarthy & Luzum 2003) contains only
13124		* 77 terms, plus additional simplifications, yet still delivers
13125		* results of 1 mas accuracy at present epochs. This combination of
13126		* accuracy and size makes the IAU 2000B abridged nutation model
13127		* suitable for most practical applications.
13128		*
13129		* The function delivers a pole accurate to 1 mas from 1900 to 2100
13130		* (usually better than 1 mas, very occasionally just outside
13131		* 1 mas). The full IAU 2000A model, which is implemented in the
13132		* function jauNut00a (q.v.), delivers considerably greater accuracy
13133		* at current dates; however, to realize this improved accuracy,
13134		* corrections for the essentially unpredictable free-core-nutation
13135		* (FCN) must also be included.
13136		*
13137		* <li> The present function provides classical nutation. The
13138		* MHB_2000_SHORT algorithm, from which it is adapted, deals also
13139		* with (i) the offsets between the GCRS and mean poles and (ii) the
13140		* adjustments in longitude and obliquity due to the changed
13141		* precession rates. These additional functions, namely frame bias
13142		* and precession adjustments, are supported by the JSOFA functions
13143		* jauBi00 and jauPr00.
13144		*
13145		* <li> The MHB_2000_SHORT algorithm also provides "total" nutations,
13146		* comprising the arithmetic sum of the frame bias, precession
13147		* adjustments, and nutation (luni-solar + planetary). These total
13148		* nutations can be used in combination with an existing IAU 1976
13149		* precession implementation, such as jauPmat76, to deliver GCRS-
13150		* to-true predictions of mas accuracy at current epochs. However,
13151		* for symmetry with the jauNut00a function (q.v. for the reasons),
13152		* the JSOFA functions do not generate the "total nutations"
13153		* directly. Should they be required, they could of course easily
13154		* be generated by calling jauBi00, jauPr00 and the present function
13155		* and adding the results.
13156		*
13157		* <li> The IAU 2000B model includes "planetary bias" terms that are
13158		* fixed in size but compensate for long-period nutations. The
13159		* amplitudes quoted in McCarthy & Luzum (2003), namely
13160		* Dpsi = -1.5835 mas and Depsilon = +1.6339 mas, are optimized for
13161		* the "total nutations" method described in Note 6. The Luzum
13162		* (2001) values used in this JSOFA implementation, namely -0.135 mas
13163		* and +0.388 mas, are optimized for the "rigorous" method, where
13164		* frame bias, precession and nutation are applied separately and in
13165		* that order. During the interval 1995-2050, the JSOFA
13166		* implementation delivers a maximum error of 1.001 mas (not
13167		* including FCN).
13168		*</ol>
13169		*<p>References:
13170		*
13171		* <p>Lieske, J.H., Lederle, T., Fricke, W., Morando, B., "Expressions
13172		* for the precession quantities based upon the IAU /1976/ system of
13173		* astronomical constants", Astron.Astrophys. 58, 1-2, 1-16. (1977)
13174		*
13175		* <p>Luzum, B., private communication, 2001 (Fortran code
13176		* MHB_2000_SHORT)
13177		*
13178		* <p>McCarthy, D.D. & Luzum, B.J., "An abridged model of the
13179		* precession-nutation of the celestial pole", Cel.Mech.Dyn.Astron.
13180		* 85, 37-49 (2003)
13181		*
13182		* <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
13183		* Francou, G., Laskar, J., Astron.Astrophys. 282, 663-683 (1994)
13184		*
13185		*@version 2009 December 17
13186		*
13187		* @since Release 20101201
13188		*
13189		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13190		*/
13191		public static NutationTerms jauNut00b(double date1, double date2)
13192		{
13193		double t, el, elp, f, d, om, arg, dp, de, sarg, carg,
13194		dpsils, depsls, dpsipl, depspl;
13195		int i;
13196
13197		/* Units of 0.1 microarcsecond to radians */
13198	20	final double U2R = DAS2R / 1e7;
13199
13200		/* ---------------------------------------- */
13201		/* Fixed offsets in lieu of planetary terms */
13202		/* ---------------------------------------- */
13203
13204	20	final double DPPLAN = -0.135 * DMAS2R;
13205	20	final double DEPLAN = 0.388 * DMAS2R;
13206
13207		/* --------------------------------------------------- */
13208		/* Luni-solar nutation: argument and term coefficients */
13209		/* --------------------------------------------------- */
13210
13211		/* The units for the sine and cosine coefficients are */
13212		/* 0.1 microarcsec and the same per Julian century */
13213
13214		final class LSNutationModel
13215		{
13216		final int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
13217		final double ps,pst,pc; /* longitude sin, tsin, cos coefficients /
13218		final double ec,ect,es; /* obliquity cos, tcos, sin coefficients /
13219
13220		public LSNutationModel( int nl,int nlp,int nf,int nd,int nom,
13221		double ps, double pst, double pc,
13222	1540	double ec, double ect, double es ) {
13223	1540	this.nl = nl;this.nlp = nlp;this.nf = nf;this.nd = nd;this.nom = nom;
13224	1540	this.ps = ps;this.pst = pst;this.pc = pc;
13225	1540	this.ec = ec;this.ect = ect; this.es= es;
13226	1540	}
13227
13228		}
13229	20	LSNutationModel x[] = {
13230
13231		/* 1-10 */
13232		new LSNutationModel( 0, 0, 0, 0,1,
13233		-172064161.0, -174666.0, 33386.0, 92052331.0, 9086.0, 15377.0),
13234		new LSNutationModel( 0, 0, 2,-2,2,
13235		-13170906.0, -1675.0, -13696.0, 5730336.0, -3015.0, -4587.0),
13236		new LSNutationModel( 0, 0, 2, 0,2,-2276413.0,-234.0, 2796.0, 978459.0,-485.0,1374.0),
13237		new LSNutationModel( 0, 0, 0, 0,2,2074554.0, 207.0, -698.0,-897492.0, 470.0,-291.0),
13238		new LSNutationModel( 0, 1, 0, 0,0,1475877.0,-3633.0,11817.0, 73871.0,-184.0,-1924.0),
13239		new LSNutationModel( 0, 1, 2,-2,2,-516821.0, 1226.0, -524.0, 224386.0,-677.0,-174.0),
13240		new LSNutationModel( 1, 0, 0, 0,0, 711159.0, 73.0, -872.0, -6750.0, 0.0, 358.0),
13241		new LSNutationModel( 0, 0, 2, 0,1,-387298.0, -367.0, 380.0, 200728.0, 18.0, 318.0),
13242		new LSNutationModel( 1, 0, 2, 0,2,-301461.0, -36.0, 816.0, 129025.0, -63.0, 367.0),
13243		new LSNutationModel( 0,-1, 2,-2,2, 215829.0, -494.0, 111.0, -95929.0, 299.0, 132.0),
13244
13245		/* 11-20 */
13246		new LSNutationModel( 0, 0, 2,-2,1, 128227.0, 137.0, 181.0, -68982.0, -9.0, 39.0),
13247		new LSNutationModel(-1, 0, 2, 0,2, 123457.0, 11.0, 19.0, -53311.0, 32.0, -4.0),
13248		new LSNutationModel(-1, 0, 0, 2,0, 156994.0, 10.0, -168.0, -1235.0, 0.0, 82.0),
13249		new LSNutationModel( 1, 0, 0, 0,1, 63110.0, 63.0, 27.0, -33228.0, 0.0, -9.0),
13250		new LSNutationModel(-1, 0, 0, 0,1, -57976.0, -63.0, -189.0, 31429.0, 0.0, -75.0),
13251		new LSNutationModel(-1, 0, 2, 2,2, -59641.0, -11.0, 149.0, 25543.0, -11.0, 66.0),
13252		new LSNutationModel( 1, 0, 2, 0,1, -51613.0, -42.0, 129.0, 26366.0, 0.0, 78.0),
13253		new LSNutationModel(-2, 0, 2, 0,1, 45893.0, 50.0, 31.0, -24236.0, -10.0, 20.0),
13254		new LSNutationModel( 0, 0, 0, 2,0, 63384.0, 11.0, -150.0, -1220.0, 0.0, 29.0),
13255		new LSNutationModel( 0, 0, 2, 2,2, -38571.0, -1.0, 158.0, 16452.0, -11.0, 68.0),
13256
13257		/* 21-30 */
13258		new LSNutationModel( 0,-2, 2,-2,2, 32481.0, 0.0, 0.0, -13870.0, 0.0, 0.0),
13259		new LSNutationModel(-2, 0, 0, 2,0, -47722.0, 0.0, -18.0, 477.0, 0.0, -25.0),
13260		new LSNutationModel( 2, 0, 2, 0,2, -31046.0, -1.0, 131.0, 13238.0, -11.0, 59.0),
13261		new LSNutationModel( 1, 0, 2,-2,2, 28593.0, 0.0, -1.0, -12338.0, 10.0, -3.0),
13262		new LSNutationModel(-1, 0, 2, 0,1, 20441.0, 21.0, 10.0, -10758.0, 0.0, -3.0),
13263		new LSNutationModel( 2, 0, 0, 0,0, 29243.0, 0.0, -74.0, -609.0, 0.0, 13.0),
13264		new LSNutationModel( 0, 0, 2, 0,0, 25887.0, 0.0, -66.0, -550.0, 0.0, 11.0),
13265		new LSNutationModel( 0, 1, 0, 0,1, -14053.0, -25.0, 79.0, 8551.0, -2.0, -45.0),
13266		new LSNutationModel(-1, 0, 0, 2,1, 15164.0, 10.0, 11.0, -8001.0, 0.0, -1.0),
13267		new LSNutationModel( 0, 2, 2,-2,2, -15794.0, 72.0, -16.0, 6850.0, -42.0, -5.0),
13268
13269		/* 31-40 */
13270		new LSNutationModel( 0, 0,-2, 2,0, 21783.0, 0.0, 13.0, -167.0, 0.0, 13.0),
13271		new LSNutationModel( 1, 0, 0,-2,1, -12873.0, -10.0, -37.0, 6953.0, 0.0, -14.0),
13272		new LSNutationModel( 0,-1, 0, 0,1, -12654.0, 11.0, 63.0, 6415.0, 0.0, 26.0),
13273		new LSNutationModel(-1, 0, 2, 2,1, -10204.0, 0.0, 25.0, 5222.0, 0.0, 15.0),
13274		new LSNutationModel( 0, 2, 0, 0,0, 16707.0, -85.0, -10.0, 168.0, -1.0, 10.0),
13275		new LSNutationModel( 1, 0, 2, 2,2, -7691.0, 0.0, 44.0, 3268.0, 0.0, 19.0),
13276		new LSNutationModel(-2, 0, 2, 0,0, -11024.0, 0.0, -14.0, 104.0, 0.0, 2.0),
13277		new LSNutationModel( 0, 1, 2, 0,2, 7566.0, -21.0, -11.0, -3250.0, 0.0, -5.0),
13278		new LSNutationModel( 0, 0, 2, 2,1, -6637.0, -11.0, 25.0, 3353.0, 0.0, 14.0),
13279		new LSNutationModel( 0,-1, 2, 0,2, -7141.0, 21.0, 8.0, 3070.0, 0.0, 4.0),
13280
13281		/* 41-50 */
13282		new LSNutationModel( 0, 0, 0, 2,1, -6302.0, -11.0, 2.0, 3272.0, 0.0, 4.0),
13283		new LSNutationModel( 1, 0, 2,-2,1, 5800.0, 10.0, 2.0, -3045.0, 0.0, -1.0),
13284		new LSNutationModel( 2, 0, 2,-2,2, 6443.0, 0.0, -7.0, -2768.0, 0.0, -4.0),
13285		new LSNutationModel(-2, 0, 0, 2,1, -5774.0, -11.0, -15.0, 3041.0, 0.0, -5.0),
13286		new LSNutationModel( 2, 0, 2, 0,1, -5350.0, 0.0, 21.0, 2695.0, 0.0, 12.0),
13287		new LSNutationModel( 0,-1, 2,-2,1, -4752.0, -11.0, -3.0, 2719.0, 0.0, -3.0),
13288		new LSNutationModel( 0, 0, 0,-2,1, -4940.0, -11.0, -21.0, 2720.0, 0.0, -9.0),
13289		new LSNutationModel(-1,-1, 0, 2,0, 7350.0, 0.0, -8.0, -51.0, 0.0, 4.0),
13290		new LSNutationModel( 2, 0, 0,-2,1, 4065.0, 0.0, 6.0, -2206.0, 0.0, 1.0),
13291		new LSNutationModel( 1, 0, 0, 2,0, 6579.0, 0.0, -24.0, -199.0, 0.0, 2.0),
13292
13293		/* 51-60 */
13294		new LSNutationModel( 0, 1, 2,-2,1, 3579.0, 0.0, 5.0, -1900.0, 0.0, 1.0),
13295		new LSNutationModel( 1,-1, 0, 0,0, 4725.0, 0.0, -6.0, -41.0, 0.0, 3.0),
13296		new LSNutationModel(-2, 0, 2, 0,2, -3075.0, 0.0, -2.0, 1313.0, 0.0, -1.0),
13297		new LSNutationModel( 3, 0, 2, 0,2, -2904.0, 0.0, 15.0, 1233.0, 0.0, 7.0),
13298		new LSNutationModel( 0,-1, 0, 2,0, 4348.0, 0.0, -10.0, -81.0, 0.0, 2.0),
13299		new LSNutationModel( 1,-1, 2, 0,2, -2878.0, 0.0, 8.0, 1232.0, 0.0, 4.0),
13300		new LSNutationModel( 0, 0, 0, 1,0, -4230.0, 0.0, 5.0, -20.0, 0.0, -2.0),
13301		new LSNutationModel(-1,-1, 2, 2,2, -2819.0, 0.0, 7.0, 1207.0, 0.0, 3.0),
13302		new LSNutationModel(-1, 0, 2, 0,0, -4056.0, 0.0, 5.0, 40.0, 0.0, -2.0),
13303		new LSNutationModel( 0,-1, 2, 2,2, -2647.0, 0.0, 11.0, 1129.0, 0.0, 5.0),
13304
13305		/* 61-70 */
13306		new LSNutationModel(-2, 0, 0, 0,1, -2294.0, 0.0, -10.0, 1266.0, 0.0, -4.0),
13307		new LSNutationModel( 1, 1, 2, 0,2, 2481.0, 0.0, -7.0, -1062.0, 0.0, -3.0),
13308		new LSNutationModel( 2, 0, 0, 0,1, 2179.0, 0.0, -2.0, -1129.0, 0.0, -2.0),
13309		new LSNutationModel(-1, 1, 0, 1,0, 3276.0, 0.0, 1.0, -9.0, 0.0, 0.0),
13310		new LSNutationModel( 1, 1, 0, 0,0, -3389.0, 0.0, 5.0, 35.0, 0.0, -2.0),
13311		new LSNutationModel( 1, 0, 2, 0,0, 3339.0, 0.0, -13.0, -107.0, 0.0, 1.0),
13312		new LSNutationModel(-1, 0, 2,-2,1, -1987.0, 0.0, -6.0, 1073.0, 0.0, -2.0),
13313		new LSNutationModel( 1, 0, 0, 0,2, -1981.0, 0.0, 0.0, 854.0, 0.0, 0.0),
13314		new LSNutationModel(-1, 0, 0, 1,0, 4026.0, 0.0, -353.0, -553.0, 0.0,-139.0),
13315		new LSNutationModel( 0, 0, 2, 1,2, 1660.0, 0.0, -5.0, -710.0, 0.0, -2.0),
13316
13317		/* 71-77 */
13318		new LSNutationModel(-1, 0, 2, 4,2, -1521.0, 0.0, 9.0, 647.0, 0.0, 4.0),
13319		new LSNutationModel(-1, 1, 0, 1,1, 1314.0, 0.0, 0.0, -700.0, 0.0, 0.0),
13320		new LSNutationModel( 0,-2, 2,-2,1, -1283.0, 0.0, 0.0, 672.0, 0.0, 0.0),
13321		new LSNutationModel( 1, 0, 2, 2,1, -1331.0, 0.0, 8.0, 663.0, 0.0, 4.0),
13322		new LSNutationModel(-2, 0, 2, 2,2, 1383.0, 0.0, -2.0, -594.0, 0.0, -2.0),
13323		new LSNutationModel(-1, 0, 0, 0,2, 1405.0, 0.0, 4.0, -610.0, 0.0, 2.0),
13324		new LSNutationModel( 1, 1, 2,-2,2, 1290.0, 0.0, 0.0, -556.0, 0.0, 0.0)
13325		};
13326
13327		/* Number of terms in the series */
13328	20	final int NLS = x.length;
13329
13330		/--------------------------------------------------------------------/
13331
13332		/* Interval between fundamental epoch J2000.0 and given date (JC). */
13333	20	t = ((date1 - DJ00) + date2) / DJC;
13334
13335		/* --------------------*/
13336		/* LUNI-SOLAR NUTATION */
13337		/* --------------------*/
13338
13339		/* Fundamental (Delaunay) arguments from Simon et al. (1994) */
13340
13341		/* Mean anomaly of the Moon. */
13342	20	el = fmod(485868.249036 + (1717915923.2178) * t, TURNAS) * DAS2R;
13343
13344		/* Mean anomaly of the Sun. */
13345	20	elp = fmod(1287104.79305 + (129596581.0481) * t, TURNAS) * DAS2R;
13346
13347		/* Mean argument of the latitude of the Moon. */
13348	20	f = fmod(335779.526232 + (1739527262.8478) * t, TURNAS) * DAS2R;
13349
13350		/* Mean elongation of the Moon from the Sun. */
13351	20	d = fmod(1072260.70369 + (1602961601.2090) * t, TURNAS) * DAS2R;
13352
13353		/* Mean longitude of the ascending node of the Moon. */
13354	20	om = fmod(450160.398036 + (-6962890.5431) * t, TURNAS) * DAS2R;
13355
13356		/* Initialize the nutation values. */
13357	20	dp = 0.0;
13358	20	de = 0.0;
13359
13360		/* Summation of luni-solar nutation series (smallest terms first). */
13361	1560	for (i = NLS-1; i >= 0; i--) {
13362
13363		/* Argument and functions. */
13364	1540	arg = fmod( (double)x[i].nl * el +
13365		(double)x[i].nlp * elp +
13366		(double)x[i].nf * f +
13367		(double)x[i].nd * d +
13368		(double)x[i].nom * om, D2PI );
13369	1540	sarg = sin(arg);
13370	1540	carg = cos(arg);
13371
13372		/* Term. */
13373	1540	dp += (x[i].ps + x[i].pst * t) * sarg + x[i].pc * carg;
13374	1540	de += (x[i].ec + x[i].ect * t) * carg + x[i].es * sarg;
13375		}
13376
13377		/* Convert from 0.1 microarcsec units to radians. */
13378	20	dpsils = dp * U2R;
13379	20	depsls = de * U2R;
13380
13381		/* ------------------------------*/
13382		/* IN LIEU OF PLANETARY NUTATION */
13383		/* ------------------------------*/
13384
13385		/* Fixed offset to correct for missing terms in truncated series. */
13386	20	dpsipl = DPPLAN;
13387	20	depspl = DEPLAN;
13388
13389		/* --------*/
13390		/* RESULTS */
13391		/* --------*/
13392
13393		/* Add luni-solar and planetary components. */
13394	20	return new NutationTerms( dpsils + dpsipl,
13395		depsls + depspl);
13396
13397		}
13398
13399
13400		/**
13401		* IAU 2000A nutation with adjustments to match the IAU 2006
13402		* precession.
13403		*
13404		*<!-- Given: -->
13405		* @param date1 double TT as a 2-part Julian Date (Note 1)
13406		* @param date2 double TT as a 2-part Julian Date (Note 1)
13407		*
13408		*<!-- Returned: -->
13409		* @return nutation, luni-solar + planetary (Note 2)
13410		*
13411		*<p>Status: canonical model.
13412		*
13413		* <p>Notes:
13414		* <ol>
13415		*
13416		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
13417		* convenient way between the two arguments. For example,
13418		* JD(TT)=2450123.7 could be expressed in any of these ways,
13419		* among others:
13420		*<pre>
13421		* date1 date2
13422		*
13423		* 2450123.7 0.0 (JD method)
13424		* 2451545.0 -1421.3 (J2000 method)
13425		* 2400000.5 50123.2 (MJD method)
13426		* 2450123.5 0.2 (date & time method)
13427		*</pre>
13428		* The JD method is the most natural and convenient to use in
13429		* cases where the loss of several decimal digits of resolution
13430		* is acceptable. The J2000 method is best matched to the way
13431		* the argument is handled internally and will deliver the
13432		* optimum resolution. The MJD method and the date & time methods
13433		* are both good compromises between resolution and convenience.
13434		*
13435		* <li> The nutation components in longitude and obliquity are in radians
13436		* and with respect to the mean equinox and ecliptic of date,
13437		* IAU 2006 precession model (Hilton et al. 2006, Capitaine et al.
13438		* 2005).
13439		*
13440		* <li> The function first computes the IAU 2000A nutation, then applies
13441		* adjustments for (i) the consequences of the change in obliquity
13442		* from the IAU 1980 ecliptic to the IAU 2006 ecliptic and (ii) the
13443		* secular variation in the Earth's dynamical flattening.
13444		*
13445		* <li> The present function provides classical nutation, complementing
13446		* the IAU 2000 frame bias and IAU 2006 precession. It delivers a
13447		* pole which is at current epochs accurate to a few tens of
13448		* microarcseconds, apart from the free core nutation.
13449		*</ol>
13450		*<p>Called:<ul>
13451		* <li>{@link #jauNut00a} nutation, IAU 2000A
13452		* </ul>
13453		*<p>References:
13454		*
13455		* <p>Chapront, J., Chapront-Touze, M. & Francou, G. 2002,
13456		* Astron.Astrophys. 387, 700
13457		*
13458		* <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B. 1977,
13459		* Astron.Astrophys. 58, 1-16
13460		*
13461		* <p>Mathews, P.M., Herring, T.A., Buffet, B.A. 2002, J.Geophys.Res.
13462		* 107, B4. The MHB_2000 code itself was obtained on 9th September
13463		* 2002 from ftp//maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
13464		*
13465		* <p>Simon, J.-L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
13466		* Francou, G., Laskar, J. 1994, Astron.Astrophys. 282, 663-683
13467		*
13468		* <p>Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M. 1999,
13469		* Astron.Astrophys.Supp.Ser. 135, 111
13470		*
13471		* <p>Wallace, P.T., "Software for Implementing the IAU 2000
13472		* Resolutions", in IERS Workshop 5.1 (2002)
13473		*
13474		*@version 2008 May 24
13475		*
13476		* @since Release 20101201
13477		*
13478		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13479		*/
13480		public static NutationTerms jauNut06a(double date1, double date2)
13481		{
13482		double t, fj2;
13483
13484
13485		/* Interval between fundamental date J2000.0 and given date (JC). */
13486	48	t = ((date1 - DJ00) + date2) / DJC;
13487
13488		/* Factor correcting for secular variation of J2. */
13489	48	fj2 = -2.7774e-6 * t;
13490
13491		/* Obtain IAU 2000A nutation. */
13492	48	NutationTerms nt = jauNut00a(date1, date2);
13493
13494		/* Apply P03 adjustments (Wallace & Capitaine, 2006, Eqs.5). */
13495	48	return new NutationTerms( nt.dpsi + nt.dpsi * (0.4697e-6 + fj2),
13496		nt.deps + nt.deps * fj2);
13497
13498		}
13499
13500		/**
13501		* Nutation, IAU 1980 model.
13502		*
13503		*<p>This function is derived from the International Astronomical Union's
13504		* SOFA (Standards Of Fundamental Astronomy) software collection.
13505		*
13506		*<p>Status: canonical model.
13507		*
13508		*<!-- Given: -->
13509		* @param date1 double TT as a 2-part Julian Date (Note 1)
13510		* @param date2 double TT as a 2-part Julian Date (Note 1)
13511		*
13512		*<!-- Returned: -->
13513		* @return dpsi double <u>returned</u> nutation in longitude (radians)
13514		* deps double <u>returned</u> nutation in obliquity (radians)
13515		*
13516		* <p>Notes:
13517		* <ol>
13518		*
13519		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
13520		* convenient way between the two arguments. For example,
13521		* JD(TT)=2450123.7 could be expressed in any of these ways,
13522		* among others:
13523		*<pre>
13524		* date1 date2
13525		*
13526		* 2450123.7 0.0 (JD method)
13527		* 2451545.0 -1421.3 (J2000 method)
13528		* 2400000.5 50123.2 (MJD method)
13529		* 2450123.5 0.2 (date & time method)
13530		*</pre>
13531		* The JD method is the most natural and convenient to use in
13532		* cases where the loss of several decimal digits of resolution
13533		* is acceptable. The J2000 method is best matched to the way
13534		* the argument is handled internally and will deliver the
13535		* optimum resolution. The MJD method and the date & time methods
13536		* are both good compromises between resolution and convenience.
13537		*
13538		* <li> The nutation components are with respect to the ecliptic of
13539		* date.
13540		*</ol>
13541		*<p>Called:<ul>
13542		* <li>{@link #jauAnpm} normalize angle into range +/- pi
13543		* </ul>
13544		*<p>Reference:
13545		*
13546		* <p>Explanatory Supplement to the Astronomical Almanac,
13547		* P. Kenneth Seidelmann (ed), University Science Books (1992),
13548		* Section 3.222 (p111).
13549		*
13550		*@version 2008 September 30
13551		*
13552		* @since Release 20101201
13553		*
13554		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13555		*/
13556		public static NutationTerms jauNut80(double date1, double date2)
13557		{
13558		double t, el, elp, f, d, om, dp, de, arg, s, c;
13559		int j;
13560
13561		/* Units of 0.1 milliarcsecond to radians */
13562	10	final double U2R = DAS2R / 1e4;
13563
13564		/* ------------------------------------------------ */
13565		/* Table of multiples of arguments and coefficients */
13566		/* ------------------------------------------------ */
13567
13568		/* The units for the sine and cosine coefficients are 0.1 mas and */
13569		/* the same per Julian century */
13570
13571		final class NutationModel {
13572		final int nl,nlp,nf,nd,nom; /* coefficients of l,l',F,D,Om */
13573		final double sp,spt; /* longitude sine, 1 and t coefficients */
13574		final double ce,cet; /* obliquity cosine, 1 and t coefficients */
13575
13576		public NutationModel(int nl,int nlp,int nf,int nd,int nom,
13577		double sp,double spt,
13578	1060	double ce,double cet ) {
13579	1060	this.nl = nl;this.nlp = nlp;this.nf = nf;this.nd = nd;this.nom = nom;
13580	1060	this.sp = sp;this.spt = spt;
13581	1060	this.ce = ce;this.cet = cet;
13582	1060	}
13583		}
13584	10	NutationModel x[] = {
13585
13586		/* 1-10 */
13587		new NutationModel( 0, 0, 0, 0, 1, -171996.0, -174.2, 92025.0, 8.9 ),
13588		new NutationModel( 0, 0, 0, 0, 2, 2062.0, 0.2, -895.0, 0.5 ),
13589		new NutationModel( -2, 0, 2, 0, 1, 46.0, 0.0, -24.0, 0.0 ),
13590		new NutationModel( 2, 0, -2, 0, 0, 11.0, 0.0, 0.0, 0.0 ),
13591		new NutationModel( -2, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 ),
13592		new NutationModel( 1, -1, 0, -1, 0, -3.0, 0.0, 0.0, 0.0 ),
13593		new NutationModel( 0, -2, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 ),
13594		new NutationModel( 2, 0, -2, 0, 1, 1.0, 0.0, 0.0, 0.0 ),
13595		new NutationModel( 0, 0, 2, -2, 2, -13187.0, -1.6, 5736.0, -3.1 ),
13596		new NutationModel( 0, 1, 0, 0, 0, 1426.0, -3.4, 54.0, -0.1 ),
13597
13598		/* 11-20 */
13599		new NutationModel( 0, 1, 2, -2, 2, -517.0, 1.2, 224.0, -0.6 ),
13600		new NutationModel( 0, -1, 2, -2, 2, 217.0, -0.5, -95.0, 0.3 ),
13601		new NutationModel( 0, 0, 2, -2, 1, 129.0, 0.1, -70.0, 0.0 ),
13602		new NutationModel( 2, 0, 0, -2, 0, 48.0, 0.0, 1.0, 0.0 ),
13603		new NutationModel( 0, 0, 2, -2, 0, -22.0, 0.0, 0.0, 0.0 ),
13604		new NutationModel( 0, 2, 0, 0, 0, 17.0, -0.1, 0.0, 0.0 ),
13605		new NutationModel( 0, 1, 0, 0, 1, -15.0, 0.0, 9.0, 0.0 ),
13606		new NutationModel( 0, 2, 2, -2, 2, -16.0, 0.1, 7.0, 0.0 ),
13607		new NutationModel( 0, -1, 0, 0, 1, -12.0, 0.0, 6.0, 0.0 ),
13608		new NutationModel( -2, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 ),
13609
13610		/* 21-30 */
13611		new NutationModel( 0, -1, 2, -2, 1, -5.0, 0.0, 3.0, 0.0 ),
13612		new NutationModel( 2, 0, 0, -2, 1, 4.0, 0.0, -2.0, 0.0 ),
13613		new NutationModel( 0, 1, 2, -2, 1, 4.0, 0.0, -2.0, 0.0 ),
13614		new NutationModel( 1, 0, 0, -1, 0, -4.0, 0.0, 0.0, 0.0 ),
13615		new NutationModel( 2, 1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 ),
13616		new NutationModel( 0, 0, -2, 2, 1, 1.0, 0.0, 0.0, 0.0 ),
13617		new NutationModel( 0, 1, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 ),
13618		new NutationModel( 0, 1, 0, 0, 2, 1.0, 0.0, 0.0, 0.0 ),
13619		new NutationModel( -1, 0, 0, 1, 1, 1.0, 0.0, 0.0, 0.0 ),
13620		new NutationModel( 0, 1, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 ),
13621
13622		/* 31-40 */
13623		new NutationModel( 0, 0, 2, 0, 2, -2274.0, -0.2, 977.0, -0.5 ),
13624		new NutationModel( 1, 0, 0, 0, 0, 712.0, 0.1, -7.0, 0.0 ),
13625		new NutationModel( 0, 0, 2, 0, 1, -386.0, -0.4, 200.0, 0.0 ),
13626		new NutationModel( 1, 0, 2, 0, 2, -301.0, 0.0, 129.0, -0.1 ),
13627		new NutationModel( 1, 0, 0, -2, 0, -158.0, 0.0, -1.0, 0.0 ),
13628		new NutationModel( -1, 0, 2, 0, 2, 123.0, 0.0, -53.0, 0.0 ),
13629		new NutationModel( 0, 0, 0, 2, 0, 63.0, 0.0, -2.0, 0.0 ),
13630		new NutationModel( 1, 0, 0, 0, 1, 63.0, 0.1, -33.0, 0.0 ),
13631		new NutationModel( -1, 0, 0, 0, 1, -58.0, -0.1, 32.0, 0.0 ),
13632		new NutationModel( -1, 0, 2, 2, 2, -59.0, 0.0, 26.0, 0.0 ),
13633
13634		/* 41-50 */
13635		new NutationModel( 1, 0, 2, 0, 1, -51.0, 0.0, 27.0, 0.0 ),
13636		new NutationModel( 0, 0, 2, 2, 2, -38.0, 0.0, 16.0, 0.0 ),
13637		new NutationModel( 2, 0, 0, 0, 0, 29.0, 0.0, -1.0, 0.0 ),
13638		new NutationModel( 1, 0, 2, -2, 2, 29.0, 0.0, -12.0, 0.0 ),
13639		new NutationModel( 2, 0, 2, 0, 2, -31.0, 0.0, 13.0, 0.0 ),
13640		new NutationModel( 0, 0, 2, 0, 0, 26.0, 0.0, -1.0, 0.0 ),
13641		new NutationModel( -1, 0, 2, 0, 1, 21.0, 0.0, -10.0, 0.0 ),
13642		new NutationModel( -1, 0, 0, 2, 1, 16.0, 0.0, -8.0, 0.0 ),
13643		new NutationModel( 1, 0, 0, -2, 1, -13.0, 0.0, 7.0, 0.0 ),
13644		new NutationModel( -1, 0, 2, 2, 1, -10.0, 0.0, 5.0, 0.0 ),
13645
13646		/* 51-60 */
13647		new NutationModel( 1, 1, 0, -2, 0, -7.0, 0.0, 0.0, 0.0 ),
13648		new NutationModel( 0, 1, 2, 0, 2, 7.0, 0.0, -3.0, 0.0 ),
13649		new NutationModel( 0, -1, 2, 0, 2, -7.0, 0.0, 3.0, 0.0 ),
13650		new NutationModel( 1, 0, 2, 2, 2, -8.0, 0.0, 3.0, 0.0 ),
13651		new NutationModel( 1, 0, 0, 2, 0, 6.0, 0.0, 0.0, 0.0 ),
13652		new NutationModel( 2, 0, 2, -2, 2, 6.0, 0.0, -3.0, 0.0 ),
13653		new NutationModel( 0, 0, 0, 2, 1, -6.0, 0.0, 3.0, 0.0 ),
13654		new NutationModel( 0, 0, 2, 2, 1, -7.0, 0.0, 3.0, 0.0 ),
13655		new NutationModel( 1, 0, 2, -2, 1, 6.0, 0.0, -3.0, 0.0 ),
13656		new NutationModel( 0, 0, 0, -2, 1, -5.0, 0.0, 3.0, 0.0 ),
13657
13658		/* 61-70 */
13659		new NutationModel( 1, -1, 0, 0, 0, 5.0, 0.0, 0.0, 0.0 ),
13660		new NutationModel( 2, 0, 2, 0, 1, -5.0, 0.0, 3.0, 0.0 ),
13661		new NutationModel( 0, 1, 0, -2, 0, -4.0, 0.0, 0.0, 0.0 ),
13662		new NutationModel( 1, 0, -2, 0, 0, 4.0, 0.0, 0.0, 0.0 ),
13663		new NutationModel( 0, 0, 0, 1, 0, -4.0, 0.0, 0.0, 0.0 ),
13664		new NutationModel( 1, 1, 0, 0, 0, -3.0, 0.0, 0.0, 0.0 ),
13665		new NutationModel( 1, 0, 2, 0, 0, 3.0, 0.0, 0.0, 0.0 ),
13666		new NutationModel( 1, -1, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 ),
13667		new NutationModel( -1, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 ),
13668		new NutationModel( -2, 0, 0, 0, 1, -2.0, 0.0, 1.0, 0.0 ),
13669
13670		/* 71-80 */
13671		new NutationModel( 3, 0, 2, 0, 2, -3.0, 0.0, 1.0, 0.0 ),
13672		new NutationModel( 0, -1, 2, 2, 2, -3.0, 0.0, 1.0, 0.0 ),
13673		new NutationModel( 1, 1, 2, 0, 2, 2.0, 0.0, -1.0, 0.0 ),
13674		new NutationModel( -1, 0, 2, -2, 1, -2.0, 0.0, 1.0, 0.0 ),
13675		new NutationModel( 2, 0, 0, 0, 1, 2.0, 0.0, -1.0, 0.0 ),
13676		new NutationModel( 1, 0, 0, 0, 2, -2.0, 0.0, 1.0, 0.0 ),
13677		new NutationModel( 3, 0, 0, 0, 0, 2.0, 0.0, 0.0, 0.0 ),
13678		new NutationModel( 0, 0, 2, 1, 2, 2.0, 0.0, -1.0, 0.0 ),
13679		new NutationModel( -1, 0, 0, 0, 2, 1.0, 0.0, -1.0, 0.0 ),
13680		new NutationModel( 1, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 ),
13681
13682		/* 81-90 */
13683		new NutationModel( -2, 0, 2, 2, 2, 1.0, 0.0, -1.0, 0.0 ),
13684		new NutationModel( -1, 0, 2, 4, 2, -2.0, 0.0, 1.0, 0.0 ),
13685		new NutationModel( 2, 0, 0, -4, 0, -1.0, 0.0, 0.0, 0.0 ),
13686		new NutationModel( 1, 1, 2, -2, 2, 1.0, 0.0, -1.0, 0.0 ),
13687		new NutationModel( 1, 0, 2, 2, 1, -1.0, 0.0, 1.0, 0.0 ),
13688		new NutationModel( -2, 0, 2, 4, 2, -1.0, 0.0, 1.0, 0.0 ),
13689		new NutationModel( -1, 0, 4, 0, 2, 1.0, 0.0, 0.0, 0.0 ),
13690		new NutationModel( 1, -1, 0, -2, 0, 1.0, 0.0, 0.0, 0.0 ),
13691		new NutationModel( 2, 0, 2, -2, 1, 1.0, 0.0, -1.0, 0.0 ),
13692		new NutationModel( 2, 0, 2, 2, 2, -1.0, 0.0, 0.0, 0.0 ),
13693
13694		/* 91-100 */
13695		new NutationModel( 1, 0, 0, 2, 1, -1.0, 0.0, 0.0, 0.0 ),
13696		new NutationModel( 0, 0, 4, -2, 2, 1.0, 0.0, 0.0, 0.0 ),
13697		new NutationModel( 3, 0, 2, -2, 2, 1.0, 0.0, 0.0, 0.0 ),
13698		new NutationModel( 1, 0, 2, -2, 0, -1.0, 0.0, 0.0, 0.0 ),
13699		new NutationModel( 0, 1, 2, 0, 1, 1.0, 0.0, 0.0, 0.0 ),
13700		new NutationModel( -1, -1, 0, 2, 1, 1.0, 0.0, 0.0, 0.0 ),
13701		new NutationModel( 0, 0, -2, 0, 1, -1.0, 0.0, 0.0, 0.0 ),
13702		new NutationModel( 0, 0, 2, -1, 2, -1.0, 0.0, 0.0, 0.0 ),
13703		new NutationModel( 0, 1, 0, 2, 0, -1.0, 0.0, 0.0, 0.0 ),
13704		new NutationModel( 1, 0, -2, -2, 0, -1.0, 0.0, 0.0, 0.0 ),
13705
13706		/* 101-106 */
13707		new NutationModel( 0, -1, 2, 0, 1, -1.0, 0.0, 0.0, 0.0 ),
13708		new NutationModel( 1, 1, 0, -2, 1, -1.0, 0.0, 0.0, 0.0 ),
13709		new NutationModel( 1, 0, -2, 2, 0, -1.0, 0.0, 0.0, 0.0 ),
13710		new NutationModel( 2, 0, 0, 2, 0, 1.0, 0.0, 0.0, 0.0 ),
13711		new NutationModel( 0, 0, 2, 4, 2, -1.0, 0.0, 0.0, 0.0 ),
13712		new NutationModel( 0, 1, 0, 1, 0, 1.0, 0.0, 0.0, 0.0 )
13713		};
13714
13715		/* Number of terms in the series */
13716	10	final int NT = x.length;
13717
13718		/--------------------------------------------------------------------/
13719
13720		/* Interval between fundamental epoch J2000.0 and given date (JC). */
13721	10	t = ((date1 - DJ00) + date2) / DJC;
13722
13723		/* --------------------- */
13724		/* Fundamental arguments */
13725		/* --------------------- */
13726
13727		/* Mean longitude of Moon minus mean longitude of Moon's perigee. */
13728	20	el = jauAnpm(
13729		(485866.733 + (715922.633 + (31.310 + 0.064 * t) * t) * t)
13730	10	* DAS2R + fmod(1325.0 * t, 1.0) * D2PI);
13731
13732		/* Mean longitude of Sun minus mean longitude of Sun's perigee. */
13733	20	elp = jauAnpm(
13734		(1287099.804 + (1292581.224 + (-0.577 - 0.012 * t) * t) * t)
13735	10	* DAS2R + fmod(99.0 * t, 1.0) * D2PI);
13736
13737		/* Mean longitude of Moon minus mean longitude of Moon's node. */
13738	20	f = jauAnpm(
13739		(335778.877 + (295263.137 + (-13.257 + 0.011 * t) * t) * t)
13740	10	* DAS2R + fmod(1342.0 * t, 1.0) * D2PI);
13741
13742		/* Mean elongation of Moon from Sun. */
13743	20	d = jauAnpm(
13744		(1072261.307 + (1105601.328 + (-6.891 + 0.019 * t) * t) * t)
13745	10	* DAS2R + fmod(1236.0 * t, 1.0) * D2PI);
13746
13747		/* Longitude of the mean ascending node of the lunar orbit on the */
13748		/* ecliptic, measured from the mean equinox of date. */
13749	20	om = jauAnpm(
13750		(450160.280 + (-482890.539 + (7.455 + 0.008 * t) * t) * t)
13751	10	* DAS2R + fmod(-5.0 * t, 1.0) * D2PI);
13752
13753		/* --------------- */
13754		/* Nutation series */
13755		/* --------------- */
13756
13757		/* Initialize nutation components. */
13758	10	dp = 0.0;
13759	10	de = 0.0;
13760
13761		/* Sum the nutation terms, ending with the biggest. */
13762	1070	for (j = NT-1; j >= 0; j--) {
13763
13764		/* Form argument for current term. */
13765	1060	arg = (double)x[j].nl * el
13766		+ (double)x[j].nlp * elp
13767		+ (double)x[j].nf * f
13768		+ (double)x[j].nd * d
13769		+ (double)x[j].nom * om;
13770
13771		/* Accumulate current nutation term. */
13772	1060	s = x[j].sp + x[j].spt * t;
13773	1060	c = x[j].ce + x[j].cet * t;
13774	1060	if (s != 0.0) dp += s * sin(arg);
13775	1060	if (c != 0.0) de += c * cos(arg);
13776		}
13777
13778		/* Convert results from 0.1 mas units to radians. */
13779	10	return new NutationTerms( dp * U2R,
13780		de * U2R);
13781
13782		}
13783
13784
13785		/**
13786		* Form the matrix of nutation for a given date, IAU 1980 model.
13787		*
13788		*<p>This function is derived from the International Astronomical Union's
13789		* SOFA (Standards Of Fundamental Astronomy) software collection.
13790		*
13791		*<p>Status: support function.
13792		*
13793		*<!-- Given: -->
13794		* @param date1 double TDB date (Note 1)
13795		* @param date2 double TDB date (Note 1)
13796		*
13797		*<!-- Returned: -->
13798		* @return double[3][3] nutation matrix
13799		*
13800		* <p>Notes:
13801		* <ol>
13802		*
13803		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
13804		* convenient way between the two arguments. For example,
13805		* JD(TT)=2450123.7 could be expressed in any of these ways,
13806		* among others:
13807		*<pre>
13808		* date1 date2
13809		*
13810		* 2450123.7 0.0 (JD method)
13811		* 2451545.0 -1421.3 (J2000 method)
13812		* 2400000.5 50123.2 (MJD method)
13813		* 2450123.5 0.2 (date & time method)
13814		*</pre>
13815		* The JD method is the most natural and convenient to use in
13816		* cases where the loss of several decimal digits of resolution
13817		* is acceptable. The J2000 method is best matched to the way
13818		* the argument is handled internally and will deliver the
13819		* optimum resolution. The MJD method and the date & time methods
13820		* are both good compromises between resolution and convenience.
13821		*
13822		* <li> The matrix operates in the sense V(true) = rmatn * V(mean),
13823		* where the p-vector V(true) is with respect to the true
13824		* equatorial triad of date and the p-vector V(mean) is with
13825		* respect to the mean equatorial triad of date.
13826		*</ol>
13827		*<p>Called:<ul>
13828		* <li>{@link #jauNut80} nutation, IAU 1980
13829		* <li>{@link #jauObl80} mean obliquity, IAU 1980
13830		* <li>{@link #jauNumat} form nutation matrix
13831		* </ul>
13832		*@version 2008 May 12
13833		*
13834		* @since Release 20101201
13835		*
13836		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13837		*/
13838		public static double[][] jauNutm80(double date1, double date2)
13839		{
13840		double rmatn[][];
13841		/* Nutation components and mean obliquity. */
13842	4	NutationTerms nt = jauNut80(date1, date2);
13843	4	double epsa = jauObl80(date1, date2);
13844
13845		/* Build the rotation matrix. */
13846	4	rmatn = jauNumat(epsa, nt.dpsi, nt.deps);
13847
13848	4	return rmatn;
13849
13850		}
13851
13852
13853		/**
13854		* Mean obliquity of the ecliptic, IAU 2006 precession model.
13855		*
13856		*<p>This function is derived from the International Astronomical Union's
13857		* SOFA (Standards Of Fundamental Astronomy) software collection.
13858		*
13859		*<p>Status: canonical model.
13860		*
13861		*<!-- Given: -->
13862		* @param date1 double TT as a 2-part Julian Date (Note 1)
13863		* @param date2 double TT as a 2-part Julian Date (Note 1)
13864		*
13865		* <!-- Returned (function value): -->
13866		* @return double obliquity of the ecliptic (radians, Note 2)
13867		*
13868		* <p>Notes:
13869		* <ol>
13870		*
13871		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
13872		* convenient way between the two arguments. For example,
13873		* JD(TT)=2450123.7 could be expressed in any of these ways,
13874		* among others:
13875		*<pre>
13876		* date1 date2
13877		*
13878		* 2450123.7 0.0 (JD method)
13879		* 2451545.0 -1421.3 (J2000 method)
13880		* 2400000.5 50123.2 (MJD method)
13881		* 2450123.5 0.2 (date & time method)
13882		*</pre>
13883		* The JD method is the most natural and convenient to use in
13884		* cases where the loss of several decimal digits of resolution
13885		* is acceptable. The J2000 method is best matched to the way
13886		* the argument is handled internally and will deliver the
13887		* optimum resolution. The MJD method and the date & time methods
13888		* are both good compromises between resolution and convenience.
13889		*
13890		* <li> The result is the angle between the ecliptic and mean equator of
13891		* date date1+date2.
13892		*</ol>
13893		*<p>Reference:
13894		*
13895		* Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
13896		*
13897		*@version 2009 March 16
13898		*
13899		* @since Release 20101201
13900		*
13901		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13902		*/
13903		public static double jauObl06(double date1, double date2)
13904		{
13905		double t, eps0;
13906
13907
13908		/* Interval between fundamental date J2000.0 and given date (JC). */
13909	78	t = ((date1 - DJ00) + date2) / DJC;
13910
13911		/* Mean obliquity. */
13912	78	eps0 = (84381.406 +
13913		(-46.836769 +
13914		( -0.0001831 +
13915		( 0.00200340 +
13916		( -0.000000576 +
13917		( -0.0000000434) * t) * t) * t) * t) * t) * DAS2R;
13918
13919	78	return eps0;
13920
13921		}
13922
13923
13924		/**
13925		* Mean obliquity of the ecliptic, IAU 1980 model.
13926		*
13927		*<p>This function is derived from the International Astronomical Union's
13928		* SOFA (Standards Of Fundamental Astronomy) software collection.
13929		*
13930		*<p>Status: canonical model.
13931		*
13932		*<!-- Given: -->
13933		* @param date1 double TT as a 2-part Julian Date (Note 1)
13934		* @param date2 double TT as a 2-part Julian Date (Note 1)
13935		*
13936		* <!-- Returned (function value): -->
13937		* @return double obliquity of the ecliptic (radians, Note 2)
13938		*
13939		* <p>Notes:
13940		* <ol>
13941		*
13942		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
13943		* convenient way between the two arguments. For example,
13944		* JD(TT)=2450123.7 could be expressed in any of these ways,
13945		* among others:
13946		*<pre>
13947		* date1 date2
13948		*
13949		* 2450123.7 0.0 (JD method)
13950		* 2451545.0 -1421.3 (J2000 method)
13951		* 2400000.5 50123.2 (MJD method)
13952		* 2450123.5 0.2 (date & time method)
13953		*</pre>
13954		* The JD method is the most natural and convenient to use in
13955		* cases where the loss of several decimal digits of resolution
13956		* is acceptable. The J2000 method is best matched to the way
13957		* the argument is handled internally and will deliver the
13958		* optimum resolution. The MJD method and the date & time methods
13959		* are both good compromises between resolution and convenience.
13960		*
13961		* <li> The result is the angle between the ecliptic and mean equator of
13962		* date date1+date2.
13963		*</ol>
13964		*<p>Reference:
13965		*
13966		* <p>Explanatory Supplement to the Astronomical Almanac,
13967		* P. Kenneth Seidelmann (ed), University Science Books (1992),
13968		* Expression 3.222-1 (p114).
13969		*
13970		*@version 2009 March 16
13971		*
13972		* @since Release 20101201
13973		*
13974		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
13975		*/
13976		public static double jauObl80(double date1, double date2)
13977		{
13978		double t, eps0;
13979
13980
13981		/* Interval between fundamental epoch J2000.0 and given date (JC). */
13982	50	t = ((date1 - DJ00) + date2) / DJC;
13983
13984		/* Mean obliquity of date. */
13985	50	eps0 = DAS2R * (84381.448 +
13986		(-46.8150 +
13987		(-0.00059 +
13988		( 0.001813) * t) * t) * t);
13989
13990	50	return eps0;
13991
13992		}
13993
13994
13995		/**
13996		* equinox based precession angles.
13997		* .
13998		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 21 Nov 2011
13999		* @version $Revision$ $date$
14000		*/
14001		public static class PrecessionAngles {
14002		/** epsilon_0 obliquity at J2000.0. */
14003		public double eps0;
14004		/** psi_A luni-solar precession. */
14005		public double psia;
14006		/** omega_A inclination of equator wrt J2000.0 ecliptic. */
14007		public double oma;
14008		/** P_A ecliptic pole x, J2000.0 ecliptic triad. */
14009		public double bpa;
14010		/** Q_A ecliptic pole -y, J2000.0 ecliptic triad. */
14011		public double bqa;
14012		/** pi_A angle between moving and J2000.0 ecliptics. */
14013		public double pia;
14014		/** Pi_A longitude of ascending node of the ecliptic. */
14015		public double bpia;
14016		/** epsilon_A obliquity of the ecliptic. */
14017		public double epsa;
14018		/** chi_A planetary precession. */
14019		public double chia;
14020		/** z_A equatorial precession: -3rd 323 Euler angle. */
14021		public double za;
14022		/** zeta_A equatorial precession: -1st 323 Euler angle. */
14023		public double zetaa;
14024		/** theta_A equatorial precession: 2nd 323 Euler angle. */
14025		public double thetaa;
14026		/** p_A general precession. */
14027		public double pa;
14028		/** gamma_J2000 J2000.0 RA difference of ecliptic poles. */
14029		public double gam;
14030		/** phi_J2000 J2000.0 codeclination of ecliptic pole. */
14031		public double phi;
14032		/** psi_J2000 longitude difference of equator poles, J2000.0. */
14033		public double psi;
14034
14035		public PrecessionAngles ( double eps0, double psia, double oma, double bpa,
14036		double bqa, double pia, double bpia,
14037		double epsa, double chia, double za, double zetaa,
14038		double thetaa, double pa,
14039	2	double gam, double phi, double psi){
14040
14041	2	this.eps0 = eps0;
14042	2	this.psia = psia;
14043	2	this.oma = oma;
14044	2	this.bpa = bpa;
14045	2	this.bqa = bqa;
14046	2	this.pia = pia;
14047	2	this.bpia = bpia;
14048	2	this.epsa = epsa;
14049	2	this.chia = chia;
14050	2	this.za = za;
14051	2	this.zetaa = zetaa;
14052	2	this.thetaa = thetaa;
14053	2	this.pa = pa;
14054	2	this.gam = gam;
14055	2	this.phi = phi;
14056	2	this.psi = psi;
14057	2	}
14058		}
14059		/**
14060		* Precession angles, IAU 2006, equinox based.
14061		*
14062		*<p>This function is derived from the International Astronomical Union's
14063		* SOFA (Standards Of Fundamental Astronomy) software collection.
14064		*
14065		*<p>Status: canonical models.
14066		*
14067		*<!-- Given: -->
14068		* @param date1 double TT as a 2-part Julian Date (Note 1)
14069		* @param date2 double TT as a 2-part Julian Date (Note 1)
14070		*
14071		* Returned (see Note 2):
14072		* eps0 double epsilon_0
14073		* psia double psi_A
14074		* oma double omega_A
14075		* bpa double P_A
14076		* bqa double Q_A
14077		* pia double pi_A
14078		* bpia double Pi_A
14079		* epsa double obliquity epsilon_A
14080		* chia double chi_A
14081		* za double z_A
14082		* zetaa double zeta_A
14083		* thetaa double theta_A
14084		* pa double p_A
14085		* gam double F-W angle gamma_J2000
14086		* phi double F-W angle phi_J2000
14087		* psi double F-W angle psi_J2000
14088		*
14089		* <p>Notes:
14090		* <ol>
14091		*
14092		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
14093		* convenient way between the two arguments. For example,
14094		* JD(TT)=2450123.7 could be expressed in any of these ways,
14095		* among others:
14096		*<pre>
14097		* date1 date2
14098		*
14099		* 2450123.7 0.0 (JD method)
14100		* 2451545.0 -1421.3 (J2000 method)
14101		* 2400000.5 50123.2 (MJD method)
14102		* 2450123.5 0.2 (date & time method)
14103		*</pre>
14104		* The JD method is the most natural and convenient to use in
14105		* cases where the loss of several decimal digits of resolution
14106		* is acceptable. The J2000 method is best matched to the way
14107		* the argument is handled internally and will deliver the
14108		* optimum resolution. The MJD method and the date & time methods
14109		* are both good compromises between resolution and convenience.
14110		*
14111		* <li> This function returns the set of equinox based angles for the
14112		* Capitaine et al. "P03" precession theory, adopted by the IAU in
14113		* 2006. The angles are set out in Table 1 of Hilton et al. (2006):
14114		*
14115		* eps0 epsilon_0 obliquity at J2000.0
14116		* psia psi_A luni-solar precession
14117		* oma omega_A inclination of equator wrt J2000.0 ecliptic
14118		* bpa P_A ecliptic pole x, J2000.0 ecliptic triad
14119		* bqa Q_A ecliptic pole -y, J2000.0 ecliptic triad
14120		* pia pi_A angle between moving and J2000.0 ecliptics
14121		* bpia Pi_A longitude of ascending node of the ecliptic
14122		* epsa epsilon_A obliquity of the ecliptic
14123		* chia chi_A planetary precession
14124		* za z_A equatorial precession: -3rd 323 Euler angle
14125		* zetaa zeta_A equatorial precession: -1st 323 Euler angle
14126		* thetaa theta_A equatorial precession: 2nd 323 Euler angle
14127		* pa p_A general precession
14128		* gam gamma_J2000 J2000.0 RA difference of ecliptic poles
14129		* phi phi_J2000 J2000.0 codeclination of ecliptic pole
14130		* psi psi_J2000 longitude difference of equator poles, J2000.0
14131		*
14132		* The returned values are all radians.
14133		*
14134		* <li> Hilton et al. (2006) Table 1 also contains angles that depend on
14135		* models distinct from the P03 precession theory itself, namely the
14136		* IAU 2000A frame bias and nutation. The quoted polynomials are
14137		* used in other JSOFA functions:
14138		*
14139		* . jauXy06 contains the polynomial parts of the X and Y series.
14140		*
14141		* . jauS06 contains the polynomial part of the s+XY/2 series.
14142		*
14143		* . jauPfw06 implements the series for the Fukushima-Williams
14144		* angles that are with respect to the GCRS pole (i.e. the variants
14145		* that include frame bias).
14146		*
14147		* <li> The IAU resolution stipulated that the choice of parameterization
14148		* was left to the user, and so an IAU compliant precession
14149		* implementation can be constructed using various combinations of
14150		* the angles returned by the present function.
14151		*
14152		* <li> The parameterization used by JSOFA is the Fukushima-Williams angles
14153		* referred directly to the GCRS pole. These are the final four
14154		* arguments returned by the present function, but are more
14155		* efficiently calculated by calling the function jauPfw06. JSOFA
14156		* also supports the direct computation of the CIP GCRS X,Y by
14157		* series, available by calling jauXy06.
14158		*
14159		* <li> The agreement between the different parameterizations is at the
14160		* 1 microarcsecond level in the present era.
14161		*
14162		* <li> When constructing a precession formulation that refers to the GCRS
14163		* pole rather than the dynamical pole, it may (depending on the
14164		* choice of angles) be necessary to introduce the frame bias
14165		* explicitly.
14166		*
14167		* <li> It is permissible to re-use the same variable in the returned
14168		* arguments. The quantities are stored in the stated order.
14169		*</ol>
14170		*<p>Reference:
14171		*
14172		* Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
14173		*
14174		*<p>Called:<ul>
14175		* <li>{@link #jauObl06} mean obliquity, IAU 2006
14176		* </ul>
14177		*@version 2009 December 17
14178		*
14179		* @since Release 20101201
14180		*
14181		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14182		*/
14183		public static PrecessionAngles jauP06e(double date1, double date2)
14184		{
14185		double t;
14186		double eps0, psia, oma, bpa,
14187		bqa, pia, bpia,
14188		epsa, chia, za, zetaa,
14189		thetaa, pa,
14190		gam, phi, psi;
14191
14192		/* Interval between fundamental date J2000.0 and given date (JC). */
14193	2	t = ((date1 - DJ00) + date2) / DJC;
14194
14195		/* Obliquity at J2000.0. */
14196
14197	2	eps0 = 84381.406 * DAS2R;
14198
14199		/* Luni-solar precession. */
14200
14201	2	psia = ( 5038.481507 +
14202		( -1.0790069 +
14203		( -0.00114045 +
14204		( 0.000132851 +
14205		( -0.0000000951 )
14206		* t) * t) * t) * t) * t * DAS2R;
14207
14208		/* Inclination of mean equator with respect to the J2000.0 ecliptic. */
14209
14210	2	oma = eps0 + ( -0.025754 +
14211		( 0.0512623 +
14212		( -0.00772503 +
14213		( -0.000000467 +
14214		( 0.0000003337 )
14215		* t) * t) * t) * t) * t * DAS2R;
14216
14217		/* Ecliptic pole x, J2000.0 ecliptic triad. */
14218
14219	2	bpa = ( 4.199094 +
14220		( 0.1939873 +
14221		( -0.00022466 +
14222		( -0.000000912 +
14223		( 0.0000000120 )
14224		* t) * t) * t) * t) * t * DAS2R;
14225
14226		/* Ecliptic pole -y, J2000.0 ecliptic triad. */
14227
14228	2	bqa = ( -46.811015 +
14229		( 0.0510283 +
14230		( 0.00052413 +
14231		( -0.000000646 +
14232		( -0.0000000172 )
14233		* t) * t) * t) * t) * t * DAS2R;
14234
14235		/* Angle between moving and J2000.0 ecliptics. */
14236
14237	2	pia = ( 46.998973 +
14238		( -0.0334926 +
14239		( -0.00012559 +
14240		( 0.000000113 +
14241		( -0.0000000022 )
14242		* t) * t) * t) * t) * t * DAS2R;
14243
14244		/* Longitude of ascending node of the moving ecliptic. */
14245
14246	2	bpia = ( 629546.7936 +
14247		( -867.95758 +
14248		( 0.157992 +
14249		( -0.0005371 +
14250		( -0.00004797 +
14251		( 0.000000072 )
14252		* t) * t) * t) * t) * t) * DAS2R;
14253
14254		/* Mean obliquity of the ecliptic. */
14255
14256	2	epsa = jauObl06(date1, date2);
14257
14258		/* Planetary precession. */
14259
14260	2	chia = ( 10.556403 +
14261		( -2.3814292 +
14262		( -0.00121197 +
14263		( 0.000170663 +
14264		( -0.0000000560 )
14265		* t) * t) * t) * t) * t * DAS2R;
14266
14267		/* Equatorial precession: minus the third of the 323 Euler angles. */
14268
14269	2	za = ( -2.650545 +
14270		( 2306.077181 +
14271		( 1.0927348 +
14272		( 0.01826837 +
14273		( -0.000028596 +
14274		( -0.0000002904 )
14275		* t) * t) * t) * t) * t) * DAS2R;
14276
14277		/* Equatorial precession: minus the first of the 323 Euler angles. */
14278
14279	2	zetaa = ( 2.650545 +
14280		( 2306.083227 +
14281		( 0.2988499 +
14282		( 0.01801828 +
14283		( -0.000005971 +
14284		( -0.0000003173 )
14285		* t) * t) * t) * t) * t) * DAS2R;
14286
14287		/* Equatorial precession: second of the 323 Euler angles. */
14288
14289	2	thetaa = ( 2004.191903 +
14290		( -0.4294934 +
14291		( -0.04182264 +
14292		( -0.000007089 +
14293		( -0.0000001274 )
14294		* t) * t) * t) * t) * t * DAS2R;
14295
14296		/* General precession. */
14297
14298	2	pa = ( 5028.796195 +
14299		( 1.1054348 +
14300		( 0.00007964 +
14301		( -0.000023857 +
14302		( 0.0000000383 )
14303		* t) * t) * t) * t) * t * DAS2R;
14304
14305		/* Fukushima-Williams angles for precession. */
14306
14307	2	gam = ( 10.556403 +
14308		( 0.4932044 +
14309		( -0.00031238 +
14310		( -0.000002788 +
14311		( 0.0000000260 )
14312		* t) * t) * t) * t) * t * DAS2R;
14313
14314	2	phi = eps0 + ( -46.811015 +
14315		( 0.0511269 +
14316		( 0.00053289 +
14317		( -0.000000440 +
14318		( -0.0000000176 )
14319		* t) * t) * t) * t) * t * DAS2R;
14320
14321	2	psi = ( 5038.481507 +
14322		( 1.5584176 +
14323		( -0.00018522 +
14324		( -0.000026452 +
14325		( -0.0000000148 )
14326		* t) * t) * t) * t) * t * DAS2R;
14327
14328	2	return new PrecessionAngles(eps0, psia, oma, bpa, bqa, pia, bpia, epsa, chia, za, zetaa, thetaa, pa, gam, phi, psi);
14329
14330		}
14331
14332
14333		/**
14334		* Extend a p-vector to a pv-vector by appending a zero velocity.
14335		*
14336		*<p>This function is derived from the International Astronomical Union's
14337		* SOFA (Standards Of Fundamental Astronomy) software collection.
14338		*
14339		*<p>Status: vector/matrix support function.
14340		*
14341		*<!-- Given: -->
14342		* @param p double[3] p-vector
14343		*
14344		*<!-- Returned: -->
14345		* @return pv double[2][3] <u>returned</u> pv-vector
14346		*
14347		*<p>Called:<ul>
14348		* <li>{@link #jauCp} copy p-vector
14349		* <li>{@link #jauZp} zero p-vector
14350		* </ul>
14351		*@version 2008 May 11
14352		*
14353		* @since Release 20101201
14354		*
14355		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14356		*/
14357		public static double[][] jauP2pv(double p[] )
14358		{
14359	2	double pv[][] = new double[3][3];
14360	2	jauCp(p, pv[0]);
14361	2	jauZp(pv[1]);
14362
14363	2	return pv;
14364
14365		}
14366
14367		/**
14368		* A position expressed in spherical polar coordinates.
14369		* .
14370		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 21 Nov 2011
14371		* @version $Revision$ $date$
14372		*/
14373		public static class SphericalPosition {
14374		/** longitude angle (radians) */
14375		public double theta;
14376		/** latitude angle (radians) */
14377		public double phi;
14378		/** radial distance */
14379		public double r;
14380	30	public SphericalPosition(double theta, double phi, double r) {
14381	30	this.theta = theta;
14382	30	this.phi = phi;
14383	30	this.r = r;
14384	30	}
14385		}
14386
14387		/**
14388		* P-vector to spherical polar coordinates.
14389		*
14390		*<p>This function is derived from the International Astronomical Union's
14391		* SOFA (Standards Of Fundamental Astronomy) software collection.
14392		*
14393		*<p>Status: vector/matrix support function.
14394		*
14395		*<!-- Given: -->
14396		* @param p double[3] p-vector
14397		*
14398		*<!-- Returned: -->
14399		* @return theta double <u>returned</u> longitude angle (radians)
14400		* phi double <u>returned</u> latitude angle (radians)
14401		* r double <u>returned</u> radial distance
14402		*
14403		* <p>Notes:
14404		* <ol>
14405		*
14406		* <li> If P is null, zero theta, phi and r are returned.
14407		*
14408		* <li> At either pole, zero theta is returned.
14409		*</ol>
14410		*<p>Called:<ul>
14411		* <li>{@link #jauC2s} p-vector to spherical
14412		* <li>{@link #jauPm} modulus of p-vector
14413		* </ul>
14414		*@version 2008 May 22
14415		*
14416		* @since Release 20101201
14417		*
14418		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14419		*/
14420		public static SphericalPosition jauP2s(double p[])
14421		{
14422	2	SphericalCoordinate sc = jauC2s(p);
14423	2	double r = jauPm(p);
14424
14425	2	return new SphericalPosition(sc.alpha, sc.delta, r);
14426
14427		}
14428
14429
14430		/**
14431		* Position-angle from two p-vectors.
14432		*
14433		*<p>This function is derived from the International Astronomical Union's
14434		* SOFA (Standards Of Fundamental Astronomy) software collection.
14435		*
14436		*<p>Status: vector/matrix support function.
14437		*
14438		*<!-- Given: -->
14439		* @param a double[3] direction of reference point
14440		* @param b double[3] direction of point whose PA is required
14441		*
14442		* <!-- Returned (function value): -->
14443		* @return double position angle of b with respect to a (radians)
14444		*
14445		* <p>Notes:
14446		* <ol>
14447		*
14448		* <li> The result is the position angle, in radians, of direction b with
14449		* respect to direction a. It is in the range -pi to +pi. The
14450		* sense is such that if b is a small distance "north" of a the
14451		* position angle is approximately zero, and if b is a small
14452		* distance "east" of a the position angle is approximately +pi/2.
14453		*
14454		* <li> The vectors a and b need not be of unit length.
14455		*
14456		* <li> Zero is returned if the two directions are the same or if either
14457		* vector is null.
14458		*
14459		* <li> If vector a is at a pole, the result is ill-defined.
14460		*</ol>
14461		*<p>Called:<ul>
14462		* <li>{@link #jauPn} decompose p-vector into modulus and direction
14463		* <li>{@link #jauPm} modulus of p-vector
14464		* <li>{@link #jauPxp} vector product of two p-vectors
14465		* <li>{@link #jauPmp} p-vector minus p-vector
14466		* <li>{@link #jauPdp} scalar product of two p-vectors
14467		* </ul>
14468		*@version 2008 May 25
14469		*
14470		* @since Release 20101201
14471		*
14472		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14473		*/
14474		public static double jauPap(double a[] , double b[] )
14475		{
14476	2	double am, au[] = new double[3], bm, st, ct, xa, ya, za, eta[] = new double[3], xi[] = new double[3], a2b[] = new double[3], pa;
14477
14478
14479		/* Modulus and direction of the a vector. */
14480	2	NormalizedVector nv = jauPn(a );
14481	2	am = nv.r; au = nv.u;
14482		/* Modulus of the b vector. */
14483	2	bm = jauPm(b);
14484
14485		/* Deal with the case of a null vector. */
14486	2	if ((am == 0.0) \|\| (bm == 0.0)) {
14487	0	st = 0.0;
14488	0	ct = 1.0;
14489		} else {
14490
14491		/* The "north" axis tangential from a (arbitrary length). */
14492	2	xa = a[0];
14493	2	ya = a[1];
14494	2	za = a[2];
14495	2	eta[0] = -xa * za;
14496	2	eta[1] = -ya * za;
14497	2	eta[2] = xaxa + yaya;
14498
14499		/* The "east" axis tangential from a (same length). */
14500	2	xi = jauPxp(eta,au);
14501
14502		/* The vector from a to b. */
14503	2	a2b = jauPmp(b, a);
14504
14505		/* Resolve into components along the north and east axes. */
14506	2	st = jauPdp(a2b, xi);
14507	2	ct = jauPdp(a2b, eta);
14508
14509		/* Deal with degenerate cases. */
14510	2	if ((st == 0.0) && (ct == 0.0)) ct = 1.0;
14511		}
14512
14513		/* Position angle. */
14514	2	pa = atan2(st, ct);
14515
14516	2	return pa;
14517
14518		}
14519
14520
14521		/**
14522		* Position-angle from spherical coordinates.
14523		*
14524		*<p>This function is derived from the International Astronomical Union's
14525		* SOFA (Standards Of Fundamental Astronomy) software collection.
14526		*
14527		*<p>Status: vector/matrix support function.
14528		*
14529		*<!-- Given: -->
14530		* @param al double longitude of point A (e.g. RA) in radians
14531		* @param ap double latitude of point A (e.g. Dec) in radians
14532		* @param bl double longitude of point B
14533		* @param bp double latitude of point B
14534		*
14535		* <!-- Returned (function value): -->
14536		* @return double position angle of B with respect to A
14537		*
14538		* <p>Notes:
14539		* <ol>
14540		*
14541		* <li> The result is the bearing (position angle), in radians, of point
14542		* B with respect to point A. It is in the range -pi to +pi. The
14543		* sense is such that if B is a small distance "east" of point A,
14544		* the bearing is approximately +pi/2.
14545		*
14546		* <li> Zero is returned if the two points are coincident.
14547		*</ol>
14548		*@version 2008 May 22
14549		*
14550		* @since Release 20101201
14551		*
14552		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14553		*/
14554		public static double jauPas(double al, double ap, double bl, double bp)
14555		{
14556		double dl, x, y, pa;
14557
14558
14559	2	dl = bl - al;
14560	2	y = sin(dl) * cos(bp);
14561	2	x = sin(bp) * cos(ap) - cos(bp) * sin(ap) * cos(dl);
14562	2	pa = ((x != 0.0) \|\| (y != 0.0)) ? atan2(y, x) : 0.0;
14563
14564	2	return pa;
14565
14566		}
14567
14568
14569		/**
14570		* This function forms three Euler angles which implement general
14571		* precession from epoch J2000.0, using the IAU 2006 model. Frame
14572		* bias (the offset between ICRS and mean J2000.0) is included.
14573		*
14574		*<p>This function is derived from the International Astronomical Union's
14575		* SOFA (Standards Of Fundamental Astronomy) software collection.
14576		*
14577		*<p>Status: support function.
14578		*
14579		*<!-- Given: -->
14580		* @param date1 double TT as a 2-part Julian Date (Note 1)
14581		* @param date2 double TT as a 2-part Julian Date (Note 1)
14582		*
14583		*<!-- Returned: -->
14584		* @return bzeta 1st rotation: radians cw around z,
14585		* 3rd rotation: radians cw around z,
14586		* 2nd rotation: radians ccw around y.
14587		*
14588		* <p>Notes:
14589		* <ol>
14590		*
14591		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
14592		* convenient way between the two arguments. For example,
14593		* JD(TT)=2450123.7 could be expressed in any of these ways,
14594		* among others:
14595		*<pre>
14596		* date1 date2
14597		*
14598		* 2450123.7 0.0 (JD method)
14599		* 2451545.0 -1421.3 (J2000 method)
14600		* 2400000.5 50123.2 (MJD method)
14601		* 2450123.5 0.2 (date & time method)
14602		*</pre>
14603		* The JD method is the most natural and convenient to use in
14604		* cases where the loss of several decimal digits of resolution
14605		* is acceptable. The J2000 method is best matched to the way
14606		* the argument is handled internally and will deliver the
14607		* optimum resolution. The MJD method and the date & time methods
14608		* are both good compromises between resolution and convenience.
14609		*
14610		* <li> The traditional accumulated precession angles zeta_A, z_A,
14611		* theta_A cannot be obtained in the usual way, namely through
14612		* polynomial expressions, because of the frame bias. The latter
14613		* means that two of the angles undergo rapid changes near this
14614		* date. They are instead the results of decomposing the
14615		* precession-bias matrix obtained by using the Fukushima-Williams
14616		* method, which does not suffer from the problem. The
14617		* decomposition returns values which can be used in the
14618		* conventional formulation and which include frame bias.
14619		*
14620		* <li> The three angles are returned in the conventional order, which
14621		* is not the same as the order of the corresponding Euler
14622		* rotations. The precession-bias matrix is
14623		* R_3(-z) x R_2(+theta) x R_3(-zeta).
14624		*
14625		* <li> Should zeta_A, z_A, theta_A angles be required that do not
14626		* contain frame bias, they are available by calling the JSOFA
14627		* function jauP06e.
14628		*</ol>
14629		*<p>Called:<ul>
14630		* <li>{@link #jauPmat06} PB matrix, IAU 2006
14631		* <li>{@link #jauRz} rotate around Z-axis
14632		* </ul>
14633		*@version 2008 May 26
14634		*
14635		* @since Release 20101201
14636		*
14637		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14638		*/
14639		public static EulerAngles jauPb06(double date1, double date2)
14640		{
14641	2	double r[][] = new double[3][3], r31, r32;
14642
14643
14644		/* Precession matrix via Fukushima-Williams angles. */
14645	2	r = jauPmat06(date1, date2);
14646
14647		/* Solve for z. */
14648	2	double bz = atan2(r[1][2], r[0][2]);
14649
14650		/* Remove it from the matrix. */
14651	2	jauRz(bz, r);
14652
14653		/* Solve for the remaining two angles. */
14654	2	double bzeta = atan2 (r[1][0], r[1][1]);
14655	2	r31 = r[2][0];
14656	2	r32 = r[2][1];
14657	2	double btheta = atan2(-dsign(sqrt(r31 * r31 + r32 * r32), r[0][2]),
14658		r[2][2]);
14659
14660	2	return new EulerAngles(bzeta, bz, btheta);
14661
14662		}
14663
14664
14665		/**
14666		* p-vector inner (=scalar=dot) product.
14667		*
14668		*<p>This function is derived from the International Astronomical Union's
14669		* SOFA (Standards Of Fundamental Astronomy) software collection.
14670		*
14671		*<p>Status: vector/matrix support function.
14672		*
14673		*<!-- Given: -->
14674		* @param a double[3] first p-vector
14675		* @param b double[3] second p-vector
14676		*
14677		* <!-- Returned (function value): -->
14678		* @return double a . b
14679		*
14680		*@version 2008 May 22
14681		*
14682		* @since Release 20101201
14683		*
14684		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14685		*/
14686		public static double jauPdp(double a[] , double b[] )
14687		{
14688		double w;
14689
14690
14691	242	w = a[0] * b[0]
14692		+ a[1] * b[1]
14693		+ a[2] * b[2];
14694
14695	242	return w;
14696
14697		}
14698
14699
14700		/**
14701		* Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).
14702		*
14703		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
14704		*
14705		* @since AIDA Stage 1
14706		*/
14707		public static class FWPrecessionAngles{
14708		/** F-W angle gamma_bar (radians) */
14709		public double gamb;
14710		/** F-W angle phi_bar (radians) */
14711		public double phib;
14712		/** F-W angle psi_bar (radians) */
14713		public double psib;
14714		/** F-W angle epsilon_A (radians) */
14715		public double epsa;
14716	66	public FWPrecessionAngles(double gamb, double phib, double psib, double epsa) {
14717	66	this.gamb = gamb;
14718	66	this.phib = phib;
14719	66	this.psib = psib;
14720	66	this.epsa = epsa;
14721	66	}
14722		}
14723		/**
14724		* Precession angles, IAU 2006 (Fukushima-Williams 4-angle formulation).
14725		*
14726		*<p>This function is derived from the International Astronomical Union's
14727		* SOFA (Standards Of Fundamental Astronomy) software collection.
14728		*
14729		*<p>Status: canonical model.
14730		*
14731		*<!-- Given: -->
14732		* @param date1 double TT as a 2-part Julian Date (Note 1)
14733		* @param date2 double TT as a 2-part Julian Date (Note 1)
14734		*
14735		*<!-- Returned: -->
14736		* @return gamb double <u>returned</u> F-W angle gamma_bar (radians)
14737		* phib double <u>returned</u> F-W angle phi_bar (radians)
14738		* psib double <u>returned</u> F-W angle psi_bar (radians)
14739		* epsa double <u>returned</u> F-W angle epsilon_A (radians)
14740		*
14741		* <p>Notes:
14742		* <ol>
14743		*
14744		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
14745		* convenient way between the two arguments. For example,
14746		* JD(TT)=2450123.7 could be expressed in any of these ways,
14747		* among others:
14748		*<pre>
14749		* date1 date2
14750		*
14751		* 2450123.7 0.0 (JD method)
14752		* 2451545.0 -1421.3 (J2000 method)
14753		* 2400000.5 50123.2 (MJD method)
14754		* 2450123.5 0.2 (date & time method)
14755		*</pre>
14756		* The JD method is the most natural and convenient to use in
14757		* cases where the loss of several decimal digits of resolution
14758		* is acceptable. The J2000 method is best matched to the way
14759		* the argument is handled internally and will deliver the
14760		* optimum resolution. The MJD method and the date & time methods
14761		* are both good compromises between resolution and convenience.
14762		*
14763		* <li> Naming the following points:
14764		*
14765		* e = J2000.0 ecliptic pole,
14766		* p = GCRS pole,
14767		* E = mean ecliptic pole of date,
14768		* and P = mean pole of date,
14769		*
14770		* the four Fukushima-Williams angles are as follows:
14771		*
14772		* gamb = gamma_bar = epE
14773		* phib = phi_bar = pE
14774		* psib = psi_bar = pEP
14775		* epsa = epsilon_A = EP
14776		*
14777		* <li> The matrix representing the combined effects of frame bias and
14778		* precession is:
14779		*
14780		* PxB = R_1(-epsa).R_3(-psib).R_1(phib).R_3(gamb)
14781		*
14782		* <li> The matrix representing the combined effects of frame bias,
14783		* precession and nutation is simply:
14784		*
14785		* NxPxB = R_1(-epsa-dE).R_3(-psib-dP).R_1(phib).R_3(gamb)
14786		*
14787		* where dP and dE are the nutation components with respect to the
14788		* ecliptic of date.
14789		*</ol>
14790		*<p>Reference:
14791		*
14792		* Hilton, J. et al., 2006, Celest.Mech.Dyn.Astron. 94, 351
14793		*
14794		*<p>Called:<ul>
14795		* <li>{@link #jauObl06} mean obliquity, IAU 2006
14796		* </ul>
14797		*@version 2009 December 17
14798		*
14799		* @since Release 20101201
14800		*
14801		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
14802		*/
14803		public static FWPrecessionAngles jauPfw06(double date1, double date2 )
14804		{
14805		double t;
14806
14807
14808		/* Interval between fundamental date J2000.0 and given date (JC). */
14809	66	t = ((date1 - DJ00) + date2) / DJC;
14810
14811		/* P03 bias+precession angles. */
14812	66	double gamb = ( -0.052928 +
14813		( 10.556378 +
14814		( 0.4932044 +
14815		( -0.00031238 +
14816		( -0.000002788 +
14817		( 0.0000000260 )
14818		* t) * t) * t) * t) * t) * DAS2R;
14819	66	double phib = ( 84381.412819 +
14820		( -46.811016 +
14821		( 0.0511268 +
14822		( 0.00053289 +
14823		( -0.000000440 +
14824		( -0.0000000176 )
14825		* t) * t) * t) * t) * t) * DAS2R;
14826	66	double psib = ( -0.041775 +
14827		( 5038.481484 +
14828		( 1.5584175 +
14829		( -0.00018522 +
14830		( -0.000026452 +
14831		( -0.0000000148 )
14832		* t) * t) * t) * t) * t) * DAS2R;
14833	66	double epsa = jauObl06(date1, date2);
14834
14835	66	return new FWPrecessionAngles(gamb, phib, psib, epsa);
14836
14837		}
14838
14839
14840		/**
14841		*<p>This function is derived from the International Astronomical Union's
14842		* SOFA (Standards Of Fundamental Astronomy) software collection.
14843		*
14844		*<p>Status: support function.
14845		*
14846		* Approximate heliocentric position and velocity of a nominated major
14847		* planet: Mercury, Venus, EMB, Mars, Jupiter, Saturn, Uranus or
14848		* Neptune (but not the Earth itself).
14849		*
14850		*<!-- Given: -->
14851		* @param date1 double TDB date part A (Note 1)
14852		* @param date2 double TDB date part B (Note 1)
14853		* @param np int planet (1=Mercury, 2=Venus, 3=EMB, 4=Mars,
14854		* 5=Jupiter, 6=Saturn, 7=Uranus, 8=Neptune)
14855		*
14856		* Returned (argument):
14857		* @param pv double[3][2] (returned) planet p,v (heliocentric, J2000.0, AU,AU/d)
14858		*
14859		* <!-- Returned (function value): -->
14860		* @return int status: -1 = illegal NP (outside 1-8)
14861		* 0 = OK
14862		* +1 = warning: year outside 1000-3000
14863		* +2 = warning: failed to converge
14864		*
14865		* <p>Notes:
14866		* <ol>
14867		*
14868		* <li> The date date1+date2 is in the TDB time scale (in practice TT can
14869		* be used) and is a Julian Date, apportioned in any convenient way
14870		* between the two arguments. For example, JD(TDB)=2450123.7 could
14871		* be expressed in any of these ways, among others:
14872		*<pre>
14873		* date1 date2
14874		*
14875		* 2450123.7 0.0 (JD method)
14876		* 2451545.0 -1421.3 (J2000 method)
14877		* 2400000.5 50123.2 (MJD method)
14878		* 2450123.5 0.2 (date & time method)
14879		*</pre>
14880		* The JD method is the most natural and convenient to use in cases
14881		* where the loss of several decimal digits of resolution is
14882		* acceptable. The J2000 method is best matched to the way the
14883		* argument is handled internally and will deliver the optimum
14884		* resolution. The MJD method and the date & time methods are both
14885		* good compromises between resolution and convenience. The limited
14886		* accuracy of the present algorithm is such that any of the methods
14887		* is satisfactory.
14888		*
14889		* <li> If an np value outside the range 1-8 is supplied, an error status
14890		* (function value -1) is returned and the pv vector set to zeroes.
14891		*
14892		* <li> For np=3 the result is for the Earth-Moon Barycenter. To obtain
14893		* the heliocentric position and velocity of the Earth, use instead
14894		* the JSOFA function jauEpv00.
14895		*
14896		* <li> On successful return, the array pv contains the following:
14897		*<pre>
14898		* pv[0][0] x }
14899		* pv[1][0] y } heliocentric position, AU
14900		* pv[2][0] z }
14901		*
14902		* pv[0][1] xdot }
14903		* pv[1][1] ydot } heliocentric velocity, AU/d
14904		* pv[2][1] zdot }
14905		*</pre>
14906		* The reference frame is equatorial and is with respect to the
14907		* mean equator and equinox of epoch J2000.0.
14908		*
14909		* <li> The algorithm is due to J.L. Simon, P. Bretagnon, J. Chapront,
14910		* M. Chapront-Touze, G. Francou and J. Laskar (Bureau des
14911		* Longitudes, Paris, France). From comparisons with JPL
14912		* ephemeris DE102, they quote the following maximum errors
14913		* over the interval 1800-2050:
14914		*<pre>
14915		* L (arcsec) B (arcsec) R (km)
14916		*
14917		* Mercury 4 1 300
14918		* Venus 5 1 800
14919		* EMB 6 1 1000
14920		* Mars 17 1 7700
14921		* Jupiter 71 5 76000
14922		* Saturn 81 13 267000
14923		* Uranus 86 7 712000
14924		* Neptune 11 1 253000
14925		*</pre>
14926		* Over the interval 1000-3000, they report that the accuracy is no
14927		* worse than 1.5 times that over 1800-2050. Outside 1000-3000 the
14928		* accuracy declines.
14929		*
14930		* Comparisons of the present function with the JPL DE200 ephemeris
14931		* give the following RMS errors over the interval 1960-2025:
14932		*<pre>
14933		* position (km) velocity (m/s)
14934		*
14935		* Mercury 334 0.437
14936		* Venus 1060 0.855
14937		* EMB 2010 0.815
14938		* Mars 7690 1.98
14939		* Jupiter 71700 7.70
14940		* Saturn 199000 19.4
14941		* Uranus 564000 16.4
14942		* Neptune 158000 14.4
14943		*</pre>
14944		* Comparisons against DE200 over the interval 1800-2100 gave the
14945		* following maximum absolute differences. (The results using
14946		* DE406 were essentially the same.)
14947		*<pre>
14948		* L (arcsec) B (arcsec) R (km) Rdot (m/s)
14949		*
14950		* Mercury 7 1 500 0.7
14951		* Venus 7 1 1100 0.9
14952		* EMB 9 1 1300 1.0
14953		* Mars 26 1 9000 2.5
14954		* Jupiter 78 6 82000 8.2
14955		* Saturn 87 14 263000 24.6
14956		* Uranus 86 7 661000 27.4
14957		* Neptune 11 2 248000 21.4
14958		*</pre>
14959		* <li> The present JSOFA re-implementation of the original Simon et al.
14960		* Fortran code differs from the original in the following respects:
14961		*<ul>
14962		* <li> C instead of Fortran.
14963		*
14964		* <li> The date is supplied in two parts.
14965		*
14966		* <li> The result is returned only in equatorial Cartesian form;
14967		* the ecliptic longitude, latitude and radius vector are not
14968		* returned.
14969		*
14970		* <li> The result is in the J2000.0 equatorial frame, not ecliptic.
14971		*
14972		* <li> More is done in-line: there are fewer calls to subroutines.
14973		*
14974		* <li> Different error/warning status values are used.
14975		*
14976		* <li> A different Kepler's-equation-solver is used (avoiding
14977		* use of double precision complex).
14978		*
14979		* <li> Polynomials in t are nested to minimize rounding errors.
14980		*
14981		* <li> Explicit double constants are used to avoid mixed-mode
14982		* expressions.
14983		*</ul>
14984		* None of the above changes affects the result significantly.
14985		*
14986		* <li> The returned status indicates the most serious condition
14987		* encountered during execution of the function. Illegal np is
14988		* considered the most serious, overriding failure to converge,
14989		* which in turn takes precedence over the remote date warning.
14990		*</ol>
14991		*<p>Called:<ul>
14992		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
14993		* </ul>
14994		*<p>Reference: Simon, J.L, Bretagnon, P., Chapront, J.,
14995		* Chapront-Touze, M., Francou, G., and Laskar, J.,
14996		* Astron. Astrophys. 282, 663 (1994).
14997		*
14998		*@version 2009 December 17
14999		*
15000		* @since Release 20101201
15001		*
15002		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15003		*/
15004		public static int jauPlan94(double date1, double date2, int np, double pv[][])
15005		{
15006		/* Gaussian constant */
15007	8	final double GK = 0.017202098950;
15008
15009		/* Sin and cos of J2000.0 mean obliquity (IAU 1976) */
15010	8	final double SINEPS = 0.3977771559319137;
15011	8	final double COSEPS = 0.9174820620691818;
15012
15013		/* Maximum number of iterations allowed to solve Kepler's equation */
15014	8	final int KMAX = 10;
15015
15016		int jstat, i, k;
15017		double t, da, dl, de, dp, di, dom, dmu, arga, argl, am,
15018		ae, dae, ae2, at, r, v, si2, xq, xp, tl, xsw,
15019		xcw, xm2, xf, ci2, xms, xmc, xpxq2, x, y, z;
15020
15021		/* Planetary inverse masses */
15022	8	final double amas[] = { 6023600.0, /* Mercury */
15023		408523.5, /* Venus */
15024		328900.5, /* EMB */
15025		3098710.0, /* Mars */
15026		1047.355, /* Jupiter */
15027		3498.5, /* Saturn */
15028		22869.0, /* Uranus */
15029		19314.0 }; /* Neptune */
15030
15031		/*
15032		* Tables giving the mean Keplerian elements, limited to t^2 terms:
15033		*
15034		* a semi-major axis (AU)
15035		* dlm mean longitude (degree and arcsecond)
15036		* e eccentricity
15037		* pi longitude of the perihelion (degree and arcsecond)
15038		* dinc inclination (degree and arcsecond)
15039		* omega longitude of the ascending node (degree and arcsecond)
15040		*/
15041
15042	8	final double a[][] = {
15043		{ 0.3870983098, 0.0, 0.0 }, /* Mercury */
15044		{ 0.7233298200, 0.0, 0.0 }, /* Venus */
15045		{ 1.0000010178, 0.0, 0.0 }, /* EMB */
15046		{ 1.5236793419, 3e-10, 0.0 }, /* Mars */
15047		{ 5.2026032092, 19132e-10, -39e-10 }, /* Jupiter */
15048		{ 9.5549091915, -0.0000213896, 444e-10 }, /* Saturn */
15049		{ 19.2184460618, -3716e-10, 979e-10 }, /* Uranus */
15050		{ 30.1103868694, -16635e-10, 686e-10 } /* Neptune */
15051		};
15052
15053	8	final double dlm[][] = {
15054		{ 252.25090552, 5381016286.88982, -1.92789 },
15055		{ 181.97980085, 2106641364.33548, 0.59381 },
15056		{ 100.46645683, 1295977422.83429, -2.04411 },
15057		{ 355.43299958, 689050774.93988, 0.94264 },
15058		{ 34.35151874, 109256603.77991, -30.60378 },
15059		{ 50.07744430, 43996098.55732, 75.61614 },
15060		{ 314.05500511, 15424811.93933, -1.75083 },
15061		{ 304.34866548, 7865503.20744, 0.21103 }
15062		};
15063
15064	8	final double e[][] = {
15065		{ 0.2056317526, 0.0002040653, -28349e-10 },
15066		{ 0.0067719164, -0.0004776521, 98127e-10 },
15067		{ 0.0167086342, -0.0004203654, -0.0000126734 },
15068		{ 0.0934006477, 0.0009048438, -80641e-10 },
15069		{ 0.0484979255, 0.0016322542, -0.0000471366 },
15070		{ 0.0555481426, -0.0034664062, -0.0000643639 },
15071		{ 0.0463812221, -0.0002729293, 0.0000078913 },
15072		{ 0.0094557470, 0.0000603263, 0.0 }
15073		};
15074
15075	8	final double pi[][] = {
15076		{ 77.45611904, 5719.11590, -4.83016 },
15077		{ 131.56370300, 175.48640, -498.48184 },
15078		{ 102.93734808, 11612.35290, 53.27577 },
15079		{ 336.06023395, 15980.45908, -62.32800 },
15080		{ 14.33120687, 7758.75163, 259.95938 },
15081		{ 93.05723748, 20395.49439, 190.25952 },
15082		{ 173.00529106, 3215.56238, -34.09288 },
15083		{ 48.12027554, 1050.71912, 27.39717 }
15084		};
15085
15086	8	final double dinc[][] = {
15087		{ 7.00498625, -214.25629, 0.28977 },
15088		{ 3.39466189, -30.84437, -11.67836 },
15089		{ 0.0, 469.97289, -3.35053 },
15090		{ 1.84972648, -293.31722, -8.11830 },
15091		{ 1.30326698, -71.55890, 11.95297 },
15092		{ 2.48887878, 91.85195, -17.66225 },
15093		{ 0.77319689, -60.72723, 1.25759 },
15094		{ 1.76995259, 8.12333, 0.08135 }
15095		};
15096
15097	8	final double omega[][] = {
15098		{ 48.33089304, -4515.21727, -31.79892 },
15099		{ 76.67992019, -10008.48154, -51.32614 },
15100		{ 174.87317577, -8679.27034, 15.34191 },
15101		{ 49.55809321, -10620.90088, -230.57416 },
15102		{ 100.46440702, 6362.03561, 326.52178 },
15103		{ 113.66550252, -9240.19942, -66.23743 },
15104		{ 74.00595701, 2669.15033, 145.93964 },
15105		{ 131.78405702, -221.94322, -0.78728 }
15106		};
15107
15108		/* Tables for trigonometric terms to be added to the mean elements of */
15109		/* the semi-major axes */
15110
15111	8	final double kp[][] = {
15112		{ 69613, 75645, 88306, 59899, 15746, 71087, 142173, 3086, 0 },
15113		{ 21863, 32794, 26934, 10931, 26250, 43725, 53867, 28939, 0 },
15114		{ 16002, 21863, 32004, 10931, 14529, 16368, 15318, 32794, 0 },
15115		{ 6345, 7818, 15636, 7077, 8184, 14163, 1107, 4872, 0 },
15116		{ 1760, 1454, 1167, 880, 287, 2640, 19, 2047, 1454 },
15117		{ 574, 0, 880, 287, 19, 1760, 1167, 306, 574 },
15118		{ 204, 0, 177, 1265, 4, 385, 200, 208, 204 },
15119		{ 0, 102, 106, 4, 98, 1367, 487, 204, 0 }
15120		};
15121
15122	8	final double ca[][] = {
15123		{ 4, -13, 11, -9, -9, -3, -1, 4, 0 },
15124		{ -156, 59, -42, 6, 19, -20, -10, -12, 0 },
15125		{ 64, -152, 62, -8, 32, -41, 19, -11, 0 },
15126		{ 124, 621, -145, 208, 54, -57, 30, 15, 0 },
15127		{ -23437, -2634, 6601, 6259, -1507,-1821, 2620, -2115, -1489 },
15128		{ 62911,-119919, 79336,17814,-24241,12068, 8306, -4893, 8902 },
15129		{ 389061,-262125,-44088, 8387,-22976,-2093, -615, -9720, 6633 },
15130		{ -412235,-157046,-31430,37817, -9740, -13, -7449, 9644, 0 }
15131		};
15132
15133	8	final double sa[][] = {
15134		{ -29, -1, 9, 6, -6, 5, 4, 0, 0 },
15135		{ -48, -125, -26, -37, 18, -13, -20, -2, 0 },
15136		{ -150, -46, 68, 54, 14, 24, -28, 22, 0 },
15137		{ -621, 532, -694, -20, 192, -94, 71, -73, 0 },
15138		{ -14614,-19828, -5869, 1881, -4372, -2255, 782, 930, 913 },
15139		{ 139737, 0, 24667, 51123, -5102, 7429, -4095, -1976, -9566 },
15140		{ -138081, 0, 37205,-49039,-41901,-33872,-27037,-12474, 18797 },
15141		{ 0, 28492,133236, 69654, 52322,-49577,-26430, -3593, 0 }
15142		};
15143
15144		/* Tables giving the trigonometric terms to be added to the mean */
15145		/* elements of the mean longitudes */
15146
15147	8	final double kq[][] = {
15148		{ 3086,15746,69613,59899,75645,88306, 12661, 2658, 0, 0 },
15149		{ 21863,32794,10931, 73, 4387,26934, 1473, 2157, 0, 0 },
15150		{ 10,16002,21863,10931, 1473,32004, 4387, 73, 0, 0 },
15151		{ 10, 6345, 7818, 1107,15636, 7077, 8184, 532, 10, 0 },
15152		{ 19, 1760, 1454, 287, 1167, 880, 574, 2640, 19, 1454 },
15153		{ 19, 574, 287, 306, 1760, 12, 31, 38, 19, 574 },
15154		{ 4, 204, 177, 8, 31, 200, 1265, 102, 4, 204 },
15155		{ 4, 102, 106, 8, 98, 1367, 487, 204, 4, 102 }
15156		};
15157
15158	8	final double cl[][] = {
15159		{ 21, -95, -157, 41, -5, 42, 23, 30, 0, 0 },
15160		{ -160, -313, -235, 60, -74, -76, -27, 34, 0, 0 },
15161		{ -325, -322, -79, 232, -52, 97, 55, -41, 0, 0 },
15162		{ 2268, -979, 802, 602, -668, -33, 345, 201, -55, 0 },
15163		{ 7610, -4997,-7689,-5841,-2617, 1115,-748,-607, 6074, 354 },
15164		{ -18549, 30125,20012, -730, 824, 23,1289,-352, -14767, -2062 },
15165		{ -135245,-14594, 4197,-4030,-5630,-2898,2540,-306, 2939, 1986 },
15166		{ 89948, 2103, 8963, 2695, 3682, 1648, 866,-154, -1963, -283 }
15167		};
15168
15169	8	final double sl[][] = {
15170		{ -342, 136, -23, 62, 66, -52, -33, 17, 0, 0 },
15171		{ 524, -149, -35, 117, 151, 122, -71, -62, 0, 0 },
15172		{ -105, -137, 258, 35, -116, -88,-112, -80, 0, 0 },
15173		{ 854, -205, -936, -240, 140, -341, -97, -232, 536, 0 },
15174		{ -56980, 8016, 1012, 1448,-3024,-3710, 318, 503, 3767, 577 },
15175		{ 138606,-13478,-4964, 1441,-1319,-1482, 427, 1236, -9167, -1918 },
15176		{ 71234,-41116, 5334,-4935,-1848, 66, 434, -1748, 3780, -701 },
15177		{ -47645, 11647, 2166, 3194, 679, 0,-244, -419, -2531, 48 }
15178		};
15179
15180		/--------------------------------------------------------------------/
15181
15182		/* Validate the planet number. */
15183	8	if ((np < 1) \|\| (np > 8)) {
15184	4	jstat = -1;
15185
15186		/* Reset the result in case of failure. */
15187	12	for (k = 0; k < 2; k++) {
15188	32	for (i = 0; i < 3; i++) {
15189	24	pv[k][i] = 0.0;
15190		}
15191		}
15192
15193		} else {
15194
15195		/* Decrement the planet number to start at zero. */
15196	4	np--;
15197
15198		/* Time: Julian millennia since J2000.0. */
15199	4	t = ((date1 - DJ00) + date2) / DJM;
15200
15201		/* OK status unless remote date. */
15202	4	jstat = abs(t) <= 1.0 ? 0 : 1;
15203
15204		/* Compute the mean elements. */
15205	4	da = a[np][0] +
15206		(a[np][1] +
15207		a[np][2] * t) * t;
15208	4	dl = (3600.0 * dlm[np][0] +
15209		(dlm[np][1] +
15210		dlm[np][2] * t) * t) * DAS2R;
15211	4	de = e[np][0] +
15212		( e[np][1] +
15213		e[np][2] * t) * t;
15214	4	dp = jauAnpm((3600.0 * pi[np][0] +
15215		(pi[np][1] +
15216		pi[np][2] * t) * t) * DAS2R);
15217	4	di = (3600.0 * dinc[np][0] +
15218		(dinc[np][1] +
15219		dinc[np][2] * t) * t) * DAS2R;
15220	4	dom = jauAnpm((3600.0 * omega[np][0] +
15221		(omega[np][1] +
15222		omega[np][2] * t) * t) * DAS2R);
15223
15224		/* Apply the trigonometric terms. */
15225	4	dmu = 0.35953620 * t;
15226	36	for (k = 0; k < 8; k++) {
15227	32	arga = kp[np][k] * dmu;
15228	32	argl = kq[np][k] * dmu;
15229	32	da += (ca[np][k] * cos(arga) +
15230	32	sa[np][k] * sin(arga)) * 1e-7;
15231	32	dl += (cl[np][k] * cos(argl) +
15232	32	sl[np][k] * sin(argl)) * 1e-7;
15233		}
15234	4	arga = kp[np][8] * dmu;
15235	4	da += t * (ca[np][8] * cos(arga) +
15236	4	sa[np][8] * sin(arga)) * 1e-7;
15237	12	for (k = 8; k < 10; k++) {
15238	8	argl = kq[np][k] * dmu;
15239	8	dl += t * (cl[np][k] * cos(argl) +
15240	8	sl[np][k] * sin(argl)) * 1e-7;
15241		}
15242	4	dl = fmod(dl, D2PI);
15243
15244		/* Iterative soln. of Kepler's equation to get eccentric anomaly. */
15245	4	am = dl - dp;
15246	4	ae = am + de * sin(am);
15247	4	k = 0;
15248	4	dae = 1.0;
15249	18	while (k < KMAX && abs(dae) > 1e-12) {
15250	14	dae = (am - ae + de * sin(ae)) / (1.0 - de * cos(ae));
15251	14	ae += dae;
15252	14	k++;
15253	14	if (k == KMAX-1) jstat = 2;
15254		}
15255
15256		/* True anomaly. */
15257	4	ae2 = ae / 2.0;
15258	8	at = 2.0 * atan2(sqrt((1.0 + de) / (1.0 - de)) * sin(ae2),
15259	4	cos(ae2));
15260
15261		/* Distance (AU) and speed (radians per day). */
15262	4	r = da * (1.0 - de * cos(ae));
15263	4	v = GK * sqrt((1.0 + 1.0 / amas[np]) / (da * da * da));
15264
15265	4	si2 = sin(di / 2.0);
15266	4	xq = si2 * cos(dom);
15267	4	xp = si2 * sin(dom);
15268	4	tl = at + dp;
15269	4	xsw = sin(tl);
15270	4	xcw = cos(tl);
15271	4	xm2 = 2.0 * (xp * xcw - xq * xsw);
15272	4	xf = da / sqrt(1 - de * de);
15273	4	ci2 = cos(di / 2.0);
15274	4	xms = (de * sin(dp) + xsw) * xf;
15275	4	xmc = (de * cos(dp) + xcw) * xf;
15276	4	xpxq2 = 2 * xp * xq;
15277
15278		/* Position (J2000.0 ecliptic x,y,z in AU). */
15279	4	x = r * (xcw - xm2 * xp);
15280	4	y = r * (xsw + xm2 * xq);
15281	4	z = r * (-xm2 * ci2);
15282
15283		/* Rotate to equatorial. */
15284	4	pv[0][0] = x;
15285	4	pv[0][1] = y * COSEPS - z * SINEPS;
15286	4	pv[0][2] = y * SINEPS + z * COSEPS;
15287
15288		/* Velocity (J2000.0 ecliptic xdot,ydot,zdot in AU/d). */
15289	4	x = v * (( -1.0 + 2.0 * xp * xp) * xms + xpxq2 * xmc);
15290	4	y = v * (( 1.0 - 2.0 * xq * xq) * xmc - xpxq2 * xms);
15291	4	z = v * (2.0 * ci2 * (xp * xms + xq * xmc));
15292
15293		/* Rotate to equatorial. */
15294	4	pv[1][0] = x;
15295	4	pv[1][1] = y * COSEPS - z * SINEPS;
15296	4	pv[1][2] = y * SINEPS + z * COSEPS;
15297
15298		}
15299
15300		/* Return the status. */
15301	8	return jstat;
15302
15303		}
15304
15305
15306		/**
15307		* Modulus of p-vector.
15308		*
15309		*<p>This function is derived from the International Astronomical Union's
15310		* SOFA (Standards Of Fundamental Astronomy) software collection.
15311		*
15312		*<p>Status: vector/matrix support function.
15313		*
15314		*<!-- Given: -->
15315		* @param p double[3] p-vector
15316		*
15317		* <!-- Returned (function value): -->
15318		* @return double modulus
15319		*
15320		*@version 2008 May 22
15321		*
15322		* @since Release 20101201
15323		*
15324		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15325		*/
15326		public static double jauPm(double p[] )
15327		{
15328		double w;
15329
15330
15331	174	w = sqrt( p[0] * p[0]
15332		+ p[1] * p[1]
15333		+ p[2] * p[2] );
15334
15335	174	return w;
15336
15337		}
15338
15339
15340		/**
15341		* Precession matrix (including frame bias) from GCRS to a specified
15342		* date, IAU 2000 model.
15343		*
15344		*<p>This function is derived from the International Astronomical Union's
15345		* SOFA (Standards Of Fundamental Astronomy) software collection.
15346		*
15347		*<p>Status: support function.
15348		*
15349		*<!-- Given: -->
15350		* @param date1 double TT as a 2-part Julian Date (Note 1)
15351		* @param date2 double TT as a 2-part Julian Date (Note 1)
15352		*
15353		*<!-- Returned: -->
15354		* @return rbp double[3][3] <u>returned</u> bias-precession matrix (Note 2)
15355		*
15356		* <p>Notes:
15357		* <ol>
15358		*
15359		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
15360		* convenient way between the two arguments. For example,
15361		* JD(TT)=2450123.7 could be expressed in any of these ways,
15362		* among others:
15363		*<pre>
15364		* date1 date2
15365		*
15366		* 2450123.7 0.0 (JD method)
15367		* 2451545.0 -1421.3 (J2000 method)
15368		* 2400000.5 50123.2 (MJD method)
15369		* 2450123.5 0.2 (date & time method)
15370		*</pre>
15371		* The JD method is the most natural and convenient to use in
15372		* cases where the loss of several decimal digits of resolution
15373		* is acceptable. The J2000 method is best matched to the way
15374		* the argument is handled internally and will deliver the
15375		* optimum resolution. The MJD method and the date & time methods
15376		* are both good compromises between resolution and convenience.
15377		*
15378		* <li> The matrix operates in the sense V(date) = rbp * V(GCRS), where
15379		* the p-vector V(GCRS) is with respect to the Geocentric Celestial
15380		* Reference System (IAU, 2000) and the p-vector V(date) is with
15381		* respect to the mean equatorial triad of the given date.
15382		*</ol>
15383		*<p>Called:<ul>
15384		* <li>{@link #jauBp00} frame bias and precession matrices, IAU 2000
15385		* </ul>
15386		*<p>Reference:
15387		*
15388		* IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
15389		* 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
15390		* (2000)
15391		*
15392		*@version 2009 December 21
15393		*
15394		* @since Release 20101201
15395		*
15396		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15397		*/
15398		public static double[][] jauPmat00(double date1, double date2)
15399		{
15400	2	double rb[][] = new double[3][3], rp[][] = new double[3][3],
15401	2	rbp[][] = new double[3][3];
15402		/* Obtain the required matrix (discarding others). */
15403	2	jauBp00(date1, date2, rb, rp, rbp);
15404
15405	2	return rbp;
15406
15407		}
15408
15409
15410		/**
15411		* Precession matrix (including frame bias) from GCRS to a specified
15412		* date, IAU 2006 model.
15413		*
15414		*<p>This function is derived from the International Astronomical Union's
15415		* SOFA (Standards Of Fundamental Astronomy) software collection.
15416		*
15417		*<p>Status: support function.
15418		*
15419		*<!-- Given: -->
15420		* @param date1 double TT as a 2-part Julian Date (Note 1)
15421		* @param date2 double TT as a 2-part Julian Date (Note 1)
15422		*
15423		*<!-- Returned: -->
15424		* @return rbp double[3][3] <u>returned</u> bias-precession matrix (Note 2)
15425		*
15426		* <p>Notes:
15427		* <ol>
15428		*
15429		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
15430		* convenient way between the two arguments. For example,
15431		* JD(TT)=2450123.7 could be expressed in any of these ways,
15432		* among others:
15433		*<pre>
15434		* date1 date2
15435		*
15436		* 2450123.7 0.0 (JD method)
15437		* 2451545.0 -1421.3 (J2000 method)
15438		* 2400000.5 50123.2 (MJD method)
15439		* 2450123.5 0.2 (date & time method)
15440		*</pre>
15441		* The JD method is the most natural and convenient to use in
15442		* cases where the loss of several decimal digits of resolution
15443		* is acceptable. The J2000 method is best matched to the way
15444		* the argument is handled internally and will deliver the
15445		* optimum resolution. The MJD method and the date & time methods
15446		* are both good compromises between resolution and convenience.
15447		*
15448		* <li> The matrix operates in the sense V(date) = rbp * V(GCRS), where
15449		* the p-vector V(GCRS) is with respect to the Geocentric Celestial
15450		* Reference System (IAU, 2000) and the p-vector V(date) is with
15451		* respect to the mean equatorial triad of the given date.
15452		*</ol>
15453		*<p>Called:<ul>
15454		* <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
15455		* <li>{@link #jauFw2m} F-W angles to r-matrix
15456		* </ul>
15457		*<p>References:
15458		*
15459		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
15460		*
15461		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
15462		*
15463		*@version 2009 December 21
15464		*
15465		* @since Release 20101201
15466		*
15467		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15468		*/
15469		public static double[][] jauPmat06(double date1, double date2)
15470		{
15471
15472		/* Bias-precession Fukushima-Williams angles. */
15473	12	FWPrecessionAngles fw = jauPfw06(date1, date2);
15474
15475		/* Form the matrix. */
15476	12	double[][] rbp = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa );
15477
15478	12	return rbp;
15479
15480		}
15481
15482
15483		/**
15484		* Precession matrix from J2000.0 to a specified date, IAU 1976 model.
15485		*
15486		*<p>This function is derived from the International Astronomical Union's
15487		* SOFA (Standards Of Fundamental Astronomy) software collection.
15488		*
15489		*<p>Status: support function.
15490		*
15491		*<!-- Given: -->
15492		* @param date1 double ending date, TT (Note 1)
15493		* @param date2 double ending date, TT (Note 1)
15494		*
15495		*<!-- Returned: -->
15496		* @return rmatp double[3][3] <u>returned</u> precession matrix, J2000.0 -> date1+date2
15497		*
15498		* <p>Notes:
15499		* <ol>
15500		*
15501		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
15502		* convenient way between the two arguments. For example,
15503		* JD(TT)=2450123.7 could be expressed in any of these ways,
15504		* among others:
15505		*<pre>
15506		* date1 date2
15507		*
15508		* 2450123.7 0.0 (JD method)
15509		* 2451545.0 -1421.3 (J2000 method)
15510		* 2400000.5 50123.2 (MJD method)
15511		* 2450123.5 0.2 (date & time method)
15512		*</pre>
15513		* The JD method is the most natural and convenient to use in
15514		* cases where the loss of several decimal digits of resolution
15515		* is acceptable. The J2000 method is best matched to the way
15516		* the argument is handled internally and will deliver the
15517		* optimum resolution. The MJD method and the date & time methods
15518		* are both good compromises between resolution and convenience.
15519		*
15520		* <li> The matrix operates in the sense V(date) = RMATP * V(J2000),
15521		* where the p-vector V(J2000) is with respect to the mean
15522		* equatorial triad of epoch J2000.0 and the p-vector V(date)
15523		* is with respect to the mean equatorial triad of the given
15524		* date.
15525		*
15526		* <li> Though the matrix method itself is rigorous, the precession
15527		* angles are expressed through canonical polynomials which are
15528		* valid only for a limited time span. In addition, the IAU 1976
15529		* precession rate is known to be imperfect. The absolute accuracy
15530		* of the present formulation is better than 0.1 arcsec from
15531		* 1960AD to 2040AD, better than 1 arcsec from 1640AD to 2360AD,
15532		* and remains below 3 arcsec for the whole of the period
15533		* 500BC to 3000AD. The errors exceed 10 arcsec outside the
15534		* range 1200BC to 3900AD, exceed 100 arcsec outside 4200BC to
15535		* 5600AD and exceed 1000 arcsec outside 6800BC to 8200AD.
15536		*</ol>
15537		*<p>Called:<ul>
15538		* <li>{@link #jauPrec76} accumulated precession angles, IAU 1976
15539		* <li>{@link #jauIr} initialize r-matrix to identity
15540		* <li>{@link #jauRz} rotate around Z-axis
15541		* <li>{@link #jauRy} rotate around Y-axis
15542		* <li>{@link #jauCr} copy r-matrix
15543		* </ul>
15544		*<p>References:
15545		*
15546		* <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282.
15547		* equations (6) & (7), p283.
15548		*
15549		* Kaplan,G.H., 1981. USNO circular no. 163, pA2.
15550		*
15551		*@version 2009 December 18
15552		*
15553		* @since Release 20101201
15554		*
15555		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15556		*/
15557		public static double[][] jauPmat76(double date1, double date2)
15558		{
15559	4	double wmat[][] = new double[3][3];
15560	4	double rmatp[][] = new double[3][3];
15561
15562		/* Precession Euler angles, J2000.0 to specified date. */
15563	4	EulerAngles euler = jauPrec76(DJ00, 0.0, date1, date2);
15564
15565		/* Form the rotation matrix. */
15566	4	jauIr( wmat);
15567	4	jauRz( -euler.zeta, wmat);
15568	4	jauRy( euler.theta, wmat);
15569	4	jauRz( -euler.z, wmat);
15570	4	jauCr(wmat, rmatp);
15571
15572	4	return rmatp;
15573
15574		}
15575
15576
15577		/**
15578		* P-vector subtraction.
15579		*
15580		*<p>This function is derived from the International Astronomical Union's
15581		* SOFA (Standards Of Fundamental Astronomy) software collection.
15582		*
15583		*<p>Status: vector/matrix support function.
15584		*
15585		*<!-- Given: -->
15586		* @param a double[3] first p-vector
15587		* @param b double[3] second p-vector
15588		*
15589		*<!-- Returned: -->
15590		* @return amb double[3] <u>returned</u> a - b
15591		*
15592		* Note:
15593		* It is permissible to re-use the same array for any of the
15594		* arguments.
15595		*
15596		*@version 2008 November 18
15597		*
15598		* @since Release 20101201
15599		*
15600		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15601		*/
15602		public static double[] jauPmp(double a[] , double b[] )
15603		{
15604	72	double amb[] = new double[3];
15605	72	amb[0] = a[0] - b[0];
15606	72	amb[1] = a[1] - b[1];
15607	72	amb[2] = a[2] - b[2];
15608
15609	72	return amb;
15610
15611		}
15612
15613		/**
15614		* A normalized vector with r being the modulus and u[3] being the unit vector.
15615		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
15616		*
15617		* @since AIDA Stage 1
15618		*/
15619		public static class NormalizedVector {
15620		public double r;
15621		public double u[];
15622	124	public NormalizedVector(double r, double u[] ) {
15623	124	this.r = r;
15624	124	this.u = u;
15625	124	}
15626		}
15627		/**
15628		* Convert a p-vector into modulus and unit vector.
15629		*
15630		*<p>This function is derived from the International Astronomical Union's
15631		* SOFA (Standards Of Fundamental Astronomy) software collection.
15632		*
15633		*<p>Status: vector/matrix support function.
15634		*
15635		*<!-- Given: -->
15636		* @param p double[3] p-vector
15637		*
15638		*<!-- Returned: -->
15639		* @return r double <u>returned</u> modulus
15640		* u double[3] <u>returned</u> unit vector
15641		*
15642		* <p>Notes:
15643		* <ol>
15644		*
15645		* <li> If p is null, the result is null. Otherwise the result is a unit
15646		* vector.
15647		*
15648		* <li> It is permissible to re-use the same array for any of the
15649		* arguments.
15650		*</ol>
15651		*<p>Called:<ul>
15652		* <li>{@link #jauPm} modulus of p-vector
15653		* <li>{@link #jauZp} zero p-vector
15654		* <li>{@link #jauSxp} multiply p-vector by scalar
15655		* </ul>
15656		*@version 2008 November 18
15657		*
15658		* @since Release 20101201
15659		*
15660		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15661		*/
15662		public static NormalizedVector jauPn(double p[])
15663		{
15664		double w;
15665
15666		/* Obtain the modulus and test for zero. */
15667	124	w = jauPm(p);
15668	124	NormalizedVector nv = new NormalizedVector(w, new double[3]);
15669	124	if (w == 0.0) {
15670
15671		/* Null vector. */
15672	0	jauZp(nv.u);
15673
15674		} else {
15675
15676		/* Unit vector. */
15677	124	nv.u = jauSxp(1.0/w, p);
15678		}
15679
15680
15681	124	return nv;
15682
15683		}
15684
15685
15686		/**
15687		* Precession-nutation, IAU 2000 model: a multi-purpose function,
15688		* supporting classical (equinox-based) use directly and CIO-based
15689		* use indirectly.
15690		*
15691		*<p>This function is derived from the International Astronomical Union's
15692		* SOFA (Standards Of Fundamental Astronomy) software collection.
15693		*
15694		*<p>Status: support function.
15695		*
15696		*<!-- Given: -->
15697		* @param date1 double TT as a 2-part Julian Date (Note 1)
15698		* @param date2 double TT as a 2-part Julian Date (Note 1)
15699		* @param dpsi double nutation (Note 2)
15700		* @param deps double nutation (Note 2)
15701		*
15702		*<!-- Returned: -->
15703		* @return epsa double <u>returned</u> mean obliquity (Note 3),
15704		* rb double[3][3] <u>returned</u> frame bias matrix (Note 4),
15705		* rp double[3][3] <u>returned</u> precession matrix (Note 5),
15706		* rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6),
15707		* rn double[3][3] <u>returned</u> nutation matrix (Note 7),
15708		* rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Note 8)
15709		*
15710		* <p>Notes:
15711		* <ol>
15712		*
15713		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
15714		* convenient way between the two arguments. For example,
15715		* JD(TT)=2450123.7 could be expressed in any of these ways,
15716		* among others:
15717		*<pre>
15718		* date1 date2
15719		*
15720		* 2450123.7 0.0 (JD method)
15721		* 2451545.0 -1421.3 (J2000 method)
15722		* 2400000.5 50123.2 (MJD method)
15723		* 2450123.5 0.2 (date & time method)
15724		*</pre>
15725		* The JD method is the most natural and convenient to use in
15726		* cases where the loss of several decimal digits of resolution
15727		* is acceptable. The J2000 method is best matched to the way
15728		* the argument is handled internally and will deliver the
15729		* optimum resolution. The MJD method and the date & time methods
15730		* are both good compromises between resolution and convenience.
15731		*
15732		* <li> The caller is responsible for providing the nutation components;
15733		* they are in longitude and obliquity, in radians and are with
15734		* respect to the equinox and ecliptic of date. For high-accuracy
15735		* applications, free core nutation should be included as well as
15736		* any other relevant corrections to the position of the CIP.
15737		*
15738		* <li> The returned mean obliquity is consistent with the IAU 2000
15739		* precession-nutation models.
15740		*
15741		* <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
15742		* equator and equinox by applying frame bias.
15743		*
15744		* <li> The matrix rp transforms vectors from J2000.0 mean equator and
15745		* equinox to mean equator and equinox of date by applying
15746		* precession.
15747		*
15748		* <li> The matrix rbp transforms vectors from GCRS to mean equator and
15749		* equinox of date by applying frame bias then precession. It is
15750		* the product rp x rb.
15751		*
15752		* <li> The matrix rn transforms vectors from mean equator and equinox of
15753		* date to true equator and equinox of date by applying the nutation
15754		* (luni-solar + planetary).
15755		*
15756		* <li> The matrix rbpn transforms vectors from GCRS to true equator and
15757		* equinox of date. It is the product rn x rbp, applying frame
15758		* bias, precession and nutation in that order.
15759		*
15760		* <li> It is permissible to re-use the same array in the returned
15761		* arguments. The arrays are filled in the order given.
15762		*</ol>
15763		*<p>Called:<ul>
15764		* <li>{@link #jauPr00} IAU 2000 precession adjustments
15765		* <li>{@link #jauObl80} mean obliquity, IAU 1980
15766		* <li>{@link #jauBp00} frame bias and precession matrices, IAU 2000
15767		* <li>{@link #jauCr} copy r-matrix
15768		* <li>{@link #jauNumat} form nutation matrix
15769		* <li>{@link #jauRxr} product of two r-matrices
15770		* </ul>
15771		*<p>Reference:
15772		*
15773		* <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
15774		* "Expressions for the Celestial Intermediate Pole and Celestial
15775		* Ephemeris Origin consistent with the IAU 2000A precession-
15776		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
15777		*
15778		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
15779		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
15780		*
15781		*@version 2010 January 18
15782		*
15783		* @since Release 20101201
15784		*
15785		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15786		*/
15787		public static PrecessionNutation jauPn00(double date1, double date2, double dpsi, double deps)
15788		{
15789	32	double rbpw[][] = new double[3][3], rnw[][] = new double[3][3];
15790	32	double[][] rb = new double[3][3];
15791	32	double[][] rp = new double[3][3];
15792	32	double[][] rbp = new double[3][3];
15793	32	double[][] rn = new double[3][3];
15794	32	double[][] rbpn = new double[3][3];
15795
15796
15797		/* IAU 2000 precession-rate adjustments. */
15798	32	PrecessionDeltaTerms nut = jauPr00(date1, date2);
15799
15800		/* Mean obliquity, consistent with IAU 2000 precession-nutation. */
15801	32	double epsa = jauObl80(date1, date2) + nut.depspr;
15802
15803		/* Frame bias and precession matrices and their product. */
15804	32	jauBp00(date1, date2, rb, rp, rbpw);
15805	32	jauCr(rbpw, rbp);
15806
15807		/* Nutation matrix. */
15808	32	rnw = jauNumat(epsa, dpsi, deps);
15809	32	jauCr(rnw, rn);
15810
15811		/* Bias-precession-nutation matrix (classical). */
15812	32	rbpn = jauRxr(rnw, rbpw);
15813
15814	32	return new PrecessionNutation(dpsi, deps, epsa, rb, rp, rbp, rn, rbpn);
15815
15816		}
15817
15818
15819		/**
15820		* Precession-nutation model.
15821		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
15822		*
15823		* @since AIDA Stage 1
15824		*/
15825		public static class PrecessionNutation {
15826		public NutationTerms nut;
15827		/** mean obliquity */
15828		public double epsa;
15829		/** frame bias matrix */
15830		public double rb[][];
15831		/** precession matrix */
15832		public double rp[][];
15833		/** bias-precession matrix */
15834		public double rbp[][];
15835		/** nutation matrix */
15836		public double rn[][];
15837		/** GCRS-to-true matrix */
15838		public double rbpn[][];
15839		public PrecessionNutation(double dpsi, double deps, double epsa,
15840		double rb[][], double rp[][], double rbp[][],
15841	36	double rn[][], double rbpn[][]){
15842	36	this.nut = new NutationTerms(dpsi, deps);
15843	36	this.epsa = epsa;
15844	36	this.rb = rb;
15845	36	this.rp = rp;
15846	36	this.rbp = rbp;
15847	36	this.rn = rn;
15848	36	this.rbpn = rbpn;
15849	36	}
15850
15851		}
15852		/**
15853		* Precession-nutation, IAU 2000A model: a multi-purpose function,
15854		* supporting classical (equinox-based) use directly and CIO-based
15855		* use indirectly.
15856		*
15857		*<p>This function is derived from the International Astronomical Union's
15858		* SOFA (Standards Of Fundamental Astronomy) software collection.
15859		*
15860		*<p>Status: support function.
15861		*
15862		*<!-- Given: -->
15863		* @param date1 double TT as a 2-part Julian Date (Note 1)
15864		* @param date2 double TT as a 2-part Julian Date (Note 1)
15865		*
15866		*<!-- Returned: -->
15867		* @return dpsi double <u>returned</u> nutation (Note 2)
15868		* deps double <u>returned</u> nutation (Note 2)
15869		* epsa double <u>returned</u> mean obliquity (Note 3)
15870		* rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
15871		* rp double[3][3] <u>returned</u> precession matrix (Note 5)
15872		* rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
15873		* rn double[3][3] <u>returned</u> nutation matrix (Note 7)
15874		* rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Notes 8,9)
15875		*
15876		* <p>Notes:
15877		* <ol>
15878		*
15879		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
15880		* convenient way between the two arguments. For example,
15881		* JD(TT)=2450123.7 could be expressed in any of these ways,
15882		* among others:
15883		*<pre>
15884		* date1 date2
15885		*
15886		* 2450123.7 0.0 (JD method)
15887		* 2451545.0 -1421.3 (J2000 method)
15888		* 2400000.5 50123.2 (MJD method)
15889		* 2450123.5 0.2 (date & time method)
15890		*</pre>
15891		* The JD method is the most natural and convenient to use in
15892		* cases where the loss of several decimal digits of resolution
15893		* is acceptable. The J2000 method is best matched to the way
15894		* the argument is handled internally and will deliver the
15895		* optimum resolution. The MJD method and the date & time methods
15896		* are both good compromises between resolution and convenience.
15897		*
15898		* <li> The nutation components (luni-solar + planetary, IAU 2000A) in
15899		* longitude and obliquity are in radians and with respect to the
15900		* equinox and ecliptic of date. Free core nutation is omitted;
15901		* for the utmost accuracy, use the jauPn00 function, where the
15902		* nutation components are caller-specified. For faster but
15903		* slightly less accurate results, use the jauPn00b function.
15904		*
15905		* <li> The mean obliquity is consistent with the IAU 2000 precession.
15906		*
15907		* <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
15908		* equator and equinox by applying frame bias.
15909		*
15910		* <li> The matrix rp transforms vectors from J2000.0 mean equator and
15911		* equinox to mean equator and equinox of date by applying
15912		* precession.
15913		*
15914		* <li> The matrix rbp transforms vectors from GCRS to mean equator and
15915		* equinox of date by applying frame bias then precession. It is
15916		* the product rp x rb.
15917		*
15918		* <li> The matrix rn transforms vectors from mean equator and equinox
15919		* of date to true equator and equinox of date by applying the
15920		* nutation (luni-solar + planetary).
15921		*
15922		* <li> The matrix rbpn transforms vectors from GCRS to true equator and
15923		* equinox of date. It is the product rn x rbp, applying frame
15924		* bias, precession and nutation in that order.
15925		*
15926		* <li> The X,Y,Z coordinates of the IAU 2000A Celestial Intermediate
15927		* Pole are elements (3,1-3) of the GCRS-to-true matrix,
15928		* i.e. rbpn[2][0-2].
15929		*
15930		* <li> It is permissible to re-use the same array in the returned
15931		* arguments. The arrays are filled in the order given.
15932		*</ol>
15933		*<p>Called:<ul>
15934		* <li>{@link #jauNut00a} nutation, IAU 2000A
15935		* <li>{@link #jauPn00} bias/precession/nutation results, IAU 2000
15936		* </ul>
15937		*<p>Reference:
15938		*
15939		* <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
15940		* "Expressions for the Celestial Intermediate Pole and Celestial
15941		* Ephemeris Origin consistent with the IAU 2000A precession-
15942		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
15943		*
15944		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
15945		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
15946		*
15947		*@version 2010 January 18
15948		*
15949		* @since Release 20101201
15950		*
15951		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
15952		*/
15953		public static PrecessionNutation jauPn00a(double date1, double date2)
15954		{
15955		/* Nutation. */
15956	14	NutationTerms nut = jauNut00a(date1, date2);
15957
15958		/* Remaining results. */
15959	14	return jauPn00(date1, date2, nut.dpsi, nut.deps);
15960
15961
15962		}
15963
15964
15965		/**
15966		* Precession-nutation, IAU 2000B model: a multi-purpose function,
15967		* supporting classical (equinox-based) use directly and CIO-based
15968		* use indirectly.
15969		*
15970		*<p>This function is derived from the International Astronomical Union's
15971		* SOFA (Standards Of Fundamental Astronomy) software collection.
15972		*
15973		*<p>Status: support function.
15974		*
15975		*<!-- Given: -->
15976		* @param date1 double TT as a 2-part Julian Date (Note 1)
15977		* @param date2 double TT as a 2-part Julian Date (Note 1)
15978		*
15979		*<!-- Returned: -->
15980		* @return dpsi,deps double <u>returned</u> nutation (Note 2)
15981		* epsa double <u>returned</u> mean obliquity (Note 3)
15982		* rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
15983		* rp double[3][3] <u>returned</u> precession matrix (Note 5)
15984		* rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
15985		* rn double[3][3] <u>returned</u> nutation matrix (Note 7)
15986		* rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Notes 8,9)
15987		*
15988		* <p>Notes:
15989		* <ol>
15990		*
15991		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
15992		* convenient way between the two arguments. For example,
15993		* JD(TT)=2450123.7 could be expressed in any of these ways,
15994		* among others:
15995		*<pre>
15996		* date1 date2
15997		*
15998		* 2450123.7 0.0 (JD method)
15999		* 2451545.0 -1421.3 (J2000 method)
16000		* 2400000.5 50123.2 (MJD method)
16001		* 2450123.5 0.2 (date & time method)
16002		*</pre>
16003		* The JD method is the most natural and convenient to use in
16004		* cases where the loss of several decimal digits of resolution
16005		* is acceptable. The J2000 method is best matched to the way
16006		* the argument is handled internally and will deliver the
16007		* optimum resolution. The MJD method and the date & time methods
16008		* are both good compromises between resolution and convenience.
16009		*
16010		* <li> The nutation components (luni-solar + planetary, IAU 2000B) in
16011		* longitude and obliquity are in radians and with respect to the
16012		* equinox and ecliptic of date. For more accurate results, but
16013		* at the cost of increased computation, use the jauPn00a function.
16014		* For the utmost accuracy, use the jauPn00 function, where the
16015		* nutation components are caller-specified.
16016		*
16017		* <li> The mean obliquity is consistent with the IAU 2000 precession.
16018		*
16019		* <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
16020		* equator and equinox by applying frame bias.
16021		*
16022		* <li> The matrix rp transforms vectors from J2000.0 mean equator and
16023		* equinox to mean equator and equinox of date by applying
16024		* precession.
16025		*
16026		* <li> The matrix rbp transforms vectors from GCRS to mean equator and
16027		* equinox of date by applying frame bias then precession. It is
16028		* the product rp x rb.
16029		*
16030		* <li> The matrix rn transforms vectors from mean equator and equinox
16031		* of date to true equator and equinox of date by applying the
16032		* nutation (luni-solar + planetary).
16033		*
16034		* <li> The matrix rbpn transforms vectors from GCRS to true equator and
16035		* equinox of date. It is the product rn x rbp, applying frame
16036		* bias, precession and nutation in that order.
16037		*
16038		* <li> The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
16039		* Pole are elements (3,1-3) of the matrix rbpn.
16040		*
16041		* <li> It is permissible to re-use the same array in the returned
16042		* arguments. The arrays are filled in the stated order.
16043		*</ol>
16044		*<p>Called:<ul>
16045		* <li>{@link #jauNut00b} nutation, IAU 2000B
16046		* <li>{@link #jauPn00} bias/precession/nutation results, IAU 2000
16047		* </ul>
16048		*<p>Reference:
16049		*
16050		* <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
16051		* "Expressions for the Celestial Intermediate Pole and Celestial
16052		* Ephemeris Origin consistent with the IAU 2000A precession-
16053		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003).
16054		*
16055		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
16056		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
16057		*
16058		*@version 2010 January 18
16059		*
16060		* @since Release 20101201
16061		*
16062		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16063		*/
16064		public static PrecessionNutation jauPn00b(double date1, double date2)
16065		{
16066		/* Nutation. */
16067	14	NutationTerms nut = jauNut00b(date1, date2);
16068
16069		/* Remaining results. */
16070	14	return jauPn00(date1, date2, nut.dpsi, nut.deps);
16071
16072
16073		}
16074
16075
16076		/**
16077		* Precession-nutation, IAU 2006 model: a multi-purpose function,
16078		* supporting classical (equinox-based) use directly and CIO-based use
16079		* indirectly.
16080		*
16081		*<p>This function is derived from the International Astronomical Union's
16082		* SOFA (Standards Of Fundamental Astronomy) software collection.
16083		*
16084		*<p>Status: support function.
16085		*
16086		*<!-- Given: -->
16087		* @param date1 double TT as a 2-part Julian Date (Note 1)
16088		* @param date2 double TT as a 2-part Julian Date (Note 1)
16089		* @param dpsi double nutation (Note 2)
16090		* @param deps double nutation (Note 2)
16091		*
16092		*<!-- Returned: -->
16093		* @return epsa double <u>returned</u> mean obliquity (Note 3)
16094		* rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
16095		* rp double[3][3] <u>returned</u> precession matrix (Note 5)
16096		* rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
16097		* rn double[3][3] <u>returned</u> nutation matrix (Note 7)
16098		* rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Note 8)
16099		*
16100		* <p>Notes:
16101		* <ol>
16102		*
16103		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
16104		* convenient way between the two arguments. For example,
16105		* JD(TT)=2450123.7 could be expressed in any of these ways,
16106		* among others:
16107		*<pre>
16108		* date1 date2
16109		*
16110		* 2450123.7 0.0 (JD method)
16111		* 2451545.0 -1421.3 (J2000 method)
16112		* 2400000.5 50123.2 (MJD method)
16113		* 2450123.5 0.2 (date & time method)
16114		*</pre>
16115		* The JD method is the most natural and convenient to use in
16116		* cases where the loss of several decimal digits of resolution
16117		* is acceptable. The J2000 method is best matched to the way
16118		* the argument is handled internally and will deliver the
16119		* optimum resolution. The MJD method and the date & time methods
16120		* are both good compromises between resolution and convenience.
16121		*
16122		* <li> The caller is responsible for providing the nutation components;
16123		* they are in longitude and obliquity, in radians and are with
16124		* respect to the equinox and ecliptic of date. For high-accuracy
16125		* applications, free core nutation should be included as well as
16126		* any other relevant corrections to the position of the CIP.
16127		*
16128		* <li> The returned mean obliquity is consistent with the IAU 2006
16129		* precession.
16130		*
16131		* <li> The matrix rb transforms vectors from GCRS to J2000.0 mean
16132		* equator and equinox by applying frame bias.
16133		*
16134		* <li> The matrix rp transforms vectors from J2000.0 mean equator and
16135		* equinox to mean equator and equinox of date by applying
16136		* precession.
16137		*
16138		* <li> The matrix rbp transforms vectors from GCRS to mean equator and
16139		* equinox of date by applying frame bias then precession. It is
16140		* the product rp x rb.
16141		*
16142		* <li> The matrix rn transforms vectors from mean equator and equinox
16143		* of date to true equator and equinox of date by applying the
16144		* nutation (luni-solar + planetary).
16145		*
16146		* <li> The matrix rbpn transforms vectors from GCRS to true equator and
16147		* equinox of date. It is the product rn x rbp, applying frame
16148		* bias, precession and nutation in that order.
16149		*
16150		* <li> The X,Y,Z coordinates of the IAU 2000B Celestial Intermediate
16151		* Pole are elements (3,1-3) of the matrix rbpn.
16152		*
16153		* <li> It is permissible to re-use the same array in the returned
16154		* arguments. The arrays are filled in the stated order.
16155		*</ol>
16156		*<p>Called:<ul>
16157		* <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
16158		* <li>{@link #jauFw2m} F-W angles to r-matrix
16159		* <li>{@link #jauCr} copy r-matrix
16160		* <li>{@link #jauTr} transpose r-matrix
16161		* <li>{@link #jauRxr} product of two r-matrices
16162		* </ul>
16163		*<p>References:
16164		*
16165		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
16166		*
16167		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
16168		*
16169		*@version 2009 December 17
16170		*
16171		* @since Release 20101201
16172		*
16173		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16174		*/
16175		public static PrecessionNutation jauPn06(double date1, double date2, double dpsi, double deps)
16176		{
16177
16178	4	double rb[][] = new double[3][3], rbp[][] = new double[3][3], rbpn[][] = new double[3][3];
16179		/* Bias-precession Fukushima-Williams angles of J2000.0 = frame bias. */
16180	4	FWPrecessionAngles fw = jauPfw06(DJM0, DJM00);
16181
16182		/* B matrix. */
16183	4	double[][] r1 = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa);
16184	4	jauCr(r1, rb);
16185
16186		/* Bias-precession Fukushima-Williams angles of date. */
16187	4	fw = jauPfw06(date1, date2);
16188
16189		/* Bias-precession matrix. */
16190	4	double[][] r2 = jauFw2m(fw.gamb, fw.phib, fw.psib, fw.epsa );
16191	4	jauCr(r2, rbp);
16192
16193		/* Solve for precession matrix. */
16194	4	double[][] rt = jauTr(r1);
16195	4	double[][] rp = jauRxr(r2, rt);
16196
16197		/* Equinox-based bias-precession-nutation matrix. */
16198	4	r1 = jauFw2m(fw.gamb, fw.phib, fw.psib + dpsi, fw.epsa + deps);
16199	4	jauCr(r1, rbpn);
16200
16201		/* Solve for nutation matrix. */
16202	4	rt = jauTr(r2);
16203	4	double[][] rn = jauRxr(r1, rt);
16204
16205		/* Obliquity, mean of date. */
16206	4	double epsa = fw.epsa;
16207
16208	4	return new PrecessionNutation(dpsi, deps, epsa, rb, rp, rbp, rn, rbpn);
16209
16210		}
16211
16212
16213		/**
16214		* Precession-nutation, IAU 2006/2000A models: a multi-purpose function,
16215		* supporting classical (equinox-based) use directly and CIO-based use
16216		* indirectly.
16217		*
16218		*<p>This function is derived from the International Astronomical Union's
16219		* SOFA (Standards Of Fundamental Astronomy) software collection.
16220		*
16221		*<p>Status: support function.
16222		*
16223		*<!-- Given: -->
16224		* @param date1 double TT as a 2-part Julian Date (Note 1)
16225		* @param date2 double TT as a 2-part Julian Date (Note 1)
16226		*
16227		*<!-- Returned: -->
16228		* @return dpsi,deps double <u>returned</u> nutation (Note 2)
16229		* epsa double <u>returned</u> mean obliquity (Note 3)
16230		* rb double[3][3] <u>returned</u> frame bias matrix (Note 4)
16231		* rp double[3][3] <u>returned</u> precession matrix (Note 5)
16232		* rbp double[3][3] <u>returned</u> bias-precession matrix (Note 6)
16233		* rn double[3][3] <u>returned</u> nutation matrix (Note 7)
16234		* rbpn double[3][3] <u>returned</u> GCRS-to-true matrix (Notes 8,9)
16235		*
16236		* <p>Notes:
16237		* <ol>
16238		*
16239		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
16240		* convenient way between the two arguments. For example,
16241		* JD(TT)=2450123.7 could be expressed in any of these ways,
16242		* among others:
16243		*<pre>
16244		* date1 date2
16245		*
16246		* 2450123.7 0.0 (JD method)
16247		* 2451545.0 -1421.3 (J2000 method)
16248		* 2400000.5 50123.2 (MJD method)
16249		* 2450123.5 0.2 (date & time method)
16250		*</pre>
16251		* The JD method is the most natural and convenient to use in
16252		* cases where the loss of several decimal digits of resolution
16253		* is acceptable. The J2000 method is best matched to the way
16254		* the argument is handled internally and will deliver the
16255		* optimum resolution. The MJD method and the date & time methods
16256		* are both good compromises between resolution and convenience.
16257		*
16258		* <li> The nutation components (luni-solar + planetary, IAU 2000A) in
16259		* longitude and obliquity are in radians and with respect to the
16260		* equinox and ecliptic of date. Free core nutation is omitted;
16261		* for the utmost accuracy, use the jauPn06 function, where the
16262		* nutation components are caller-specified.
16263		*
16264		* <li> The mean obliquity is consistent with the IAU 2006 precession.
16265		*
16266		* <li> The matrix rb transforms vectors from GCRS to mean J2000.0 by
16267		* applying frame bias.
16268		*
16269		* <li> The matrix rp transforms vectors from mean J2000.0 to mean of
16270		* date by applying precession.
16271		*
16272		* <li> The matrix rbp transforms vectors from GCRS to mean of date by
16273		* applying frame bias then precession. It is the product rp x rb.
16274		*
16275		* <li> The matrix rn transforms vectors from mean of date to true of
16276		* date by applying the nutation (luni-solar + planetary).
16277		*
16278		* <li> The matrix rbpn transforms vectors from GCRS to true of date
16279		* (CIP/equinox). It is the product rn x rbp, applying frame bias,
16280		* precession and nutation in that order.
16281		*
16282		* <li> The X,Y,Z coordinates of the IAU 2006/2000A Celestial
16283		* Intermediate Pole are elements (1,1-3) of the matrix rbpn.
16284		*
16285		* <li> It is permissible to re-use the same array in the returned
16286		* arguments. The arrays are filled in the stated order.
16287		*</ol>
16288		*<p>Called:<ul>
16289		* <li>{@link #jauNut06a} nutation, IAU 2006/2000A
16290		* <li>{@link #jauPn06} bias/precession/nutation results, IAU 2006
16291		* </ul>
16292		*<p>Reference:
16293		*
16294		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
16295		*
16296		*@version 2009 December 18
16297		*
16298		* @since Release 20101201
16299		*
16300		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16301		*/
16302		public static PrecessionNutation jauPn06a(double date1, double date2)
16303		{
16304		/* Nutation. */
16305	2	NutationTerms nut = jauNut06a(date1, date2);
16306
16307		/* Remaining results. */
16308	2	return jauPn06(date1, date2, nut.dpsi, nut.deps);
16309
16310		}
16311
16312
16313		/**
16314		* Form the matrix of precession-nutation for a given date (including
16315		* frame bias), equinox-based, IAU 2000A model.
16316		*
16317		*<p>This function is derived from the International Astronomical Union's
16318		* SOFA (Standards Of Fundamental Astronomy) software collection.
16319		*
16320		*<p>Status: support function.
16321		*
16322		*<!-- Given: -->
16323		* @param date1 double TT as a 2-part Julian Date (Note 1)
16324		* @param date2 double TT as a 2-part Julian Date (Note 1)
16325		*
16326		*<!-- Returned: -->
16327		* @return rbpn double[3][3] <u>returned</u> classical NPB matrix (Note 2)
16328		*
16329		* <p>Notes:
16330		* <ol>
16331		*
16332		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
16333		* convenient way between the two arguments. For example,
16334		* JD(TT)=2450123.7 could be expressed in any of these ways,
16335		* among others:
16336		*<pre>
16337		* date1 date2
16338		*
16339		* 2450123.7 0.0 (JD method)
16340		* 2451545.0 -1421.3 (J2000 method)
16341		* 2400000.5 50123.2 (MJD method)
16342		* 2450123.5 0.2 (date & time method)
16343		*</pre>
16344		* The JD method is the most natural and convenient to use in
16345		* cases where the loss of several decimal digits of resolution
16346		* is acceptable. The J2000 method is best matched to the way
16347		* the argument is handled internally and will deliver the
16348		* optimum resolution. The MJD method and the date & time methods
16349		* are both good compromises between resolution and convenience.
16350		*
16351		* <li> The matrix operates in the sense V(date) = rbpn * V(GCRS), where
16352		* the p-vector V(date) is with respect to the true equatorial triad
16353		* of date date1+date2 and the p-vector V(GCRS) is with respect to
16354		* the Geocentric Celestial Reference System (IAU, 2000).
16355		*
16356		* <li> A faster, but slightly less accurate result (about 1 mas), can be
16357		* obtained by using instead the jauPnm00b function.
16358		*</ol>
16359		*<p>Called:<ul>
16360		* <li>{@link #jauPn00a} bias/precession/nutation, IAU 2000A
16361		* </ul>
16362		*<p>Reference:
16363		*
16364		* IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
16365		* 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
16366		* (2000)
16367		*
16368		*@version 2009 December 21
16369		*
16370		* @since Release 20101201
16371		*
16372		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16373		*/
16374		public static double[][] jauPnm00a(double date1, double date2)
16375		{
16376
16377		/* Obtain the required matrix (discarding other results). */
16378	10	PrecessionNutation pn = jauPn00a(date1, date2);
16379	10	return pn.rbpn;
16380
16381		}
16382
16383
16384		/**
16385		* Form the matrix of precession-nutation for a given date (including
16386		* frame bias), equinox-based, IAU 2000B model.
16387		*
16388		*<p>This function is derived from the International Astronomical Union's
16389		* SOFA (Standards Of Fundamental Astronomy) software collection.
16390		*
16391		*<p>Status: support function.
16392		*
16393		*<!-- Given: -->
16394		* @param date1 double TT as a 2-part Julian Date (Note 1)
16395		* @param date2 double TT as a 2-part Julian Date (Note 1)
16396		*
16397		*<!-- Returned: -->
16398		* @return rbpn double[3][3] <u>returned</u> bias-precession-nutation matrix (Note 2)
16399		*
16400		* <p>Notes:
16401		* <ol>
16402		*
16403		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
16404		* convenient way between the two arguments. For example,
16405		* JD(TT)=2450123.7 could be expressed in any of these ways,
16406		* among others:
16407		*<pre>
16408		* date1 date2
16409		*
16410		* 2450123.7 0.0 (JD method)
16411		* 2451545.0 -1421.3 (J2000 method)
16412		* 2400000.5 50123.2 (MJD method)
16413		* 2450123.5 0.2 (date & time method)
16414		*</pre>
16415		* The JD method is the most natural and convenient to use in
16416		* cases where the loss of several decimal digits of resolution
16417		* is acceptable. The J2000 method is best matched to the way
16418		* the argument is handled internally and will deliver the
16419		* optimum resolution. The MJD method and the date & time methods
16420		* are both good compromises between resolution and convenience.
16421		*
16422		* <li> The matrix operates in the sense V(date) = rbpn * V(GCRS), where
16423		* the p-vector V(date) is with respect to the true equatorial triad
16424		* of date date1+date2 and the p-vector V(GCRS) is with respect to
16425		* the Geocentric Celestial Reference System (IAU, 2000).
16426		*
16427		* <li> The present function is faster, but slightly less accurate (about
16428		* 1 mas), than the jauPnm00a function.
16429		*</ol>
16430		*<p>Called:<ul>
16431		* <li>{@link #jauPn00b} bias/precession/nutation, IAU 2000B
16432		* </ul>
16433		*<p>Reference:
16434		*
16435		* IAU: Trans. International Astronomical Union, Vol. XXIVB; Proc.
16436		* 24th General Assembly, Manchester, UK. Resolutions B1.3, B1.6.
16437		* (2000)
16438		*
16439		*@version 2009 December 21
16440		*
16441		* @since Release 20101201
16442		*
16443		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16444		*/
16445		public static double[][] jauPnm00b(double date1, double date2)
16446		{
16447
16448		/* Obtain the required matrix (discarding other results). */
16449	10	PrecessionNutation pn = jauPn00b(date1, date2);
16450
16451	10	return pn.rbpn;
16452
16453		}
16454
16455
16456		/**
16457		* Form the matrix of precession-nutation for a given date (including
16458		* frame bias), IAU 2006 precession and IAU 2000A nutation models.
16459		*
16460		*<p>This function is derived from the International Astronomical Union's
16461		* SOFA (Standards Of Fundamental Astronomy) software collection.
16462		*
16463		*<p>Status: support function.
16464		*
16465		*<!-- Given: -->
16466		* @param date1 double TT as a 2-part Julian Date (Note 1)
16467		* @param date2 double TT as a 2-part Julian Date (Note 1)
16468		*
16469		*<!-- Returned: -->
16470		* @return rnpb double[3][3] <u>returned</u> bias-precession-nutation matrix (Note 2)
16471		*
16472		* <p>Notes:
16473		* <ol>
16474		*
16475		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
16476		* convenient way between the two arguments. For example,
16477		* JD(TT)=2450123.7 could be expressed in any of these ways,
16478		* among others:
16479		*<pre>
16480		* date1 date2
16481		*
16482		* 2450123.7 0.0 (JD method)
16483		* 2451545.0 -1421.3 (J2000 method)
16484		* 2400000.5 50123.2 (MJD method)
16485		* 2450123.5 0.2 (date & time method)
16486		*</pre>
16487		* The JD method is the most natural and convenient to use in
16488		* cases where the loss of several decimal digits of resolution
16489		* is acceptable. The J2000 method is best matched to the way
16490		* the argument is handled internally and will deliver the
16491		* optimum resolution. The MJD method and the date & time methods
16492		* are both good compromises between resolution and convenience.
16493		*
16494		* <li> The matrix operates in the sense V(date) = rnpb * V(GCRS), where
16495		* the p-vector V(date) is with respect to the true equatorial triad
16496		* of date date1+date2 and the p-vector V(GCRS) is with respect to
16497		* the Geocentric Celestial Reference System (IAU, 2000).
16498		*</ol>
16499		*<p>Called:<ul>
16500		* <li>{@link #jauPfw06} bias-precession F-W angles, IAU 2006
16501		* <li>{@link #jauNut06a} nutation, IAU 2006/2000A
16502		* <li>{@link #jauFw2m} F-W angles to r-matrix
16503		* </ul>
16504		*<p>Reference:
16505		*
16506		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855.
16507		*
16508		*@version 2009 December 21
16509		*
16510		* @since Release 20101201
16511		*
16512		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16513		*/
16514		public static double[][] jauPnm06a(double date1, double date2)
16515		{
16516
16517		/* Fukushima-Williams angles for frame bias and precession. */
16518	42	FWPrecessionAngles fw = jauPfw06(date1, date2);
16519
16520		/* Nutation components. */
16521	42	NutationTerms nut = jauNut06a(date1, date2);
16522
16523		/* Equinox based nutation x precession x bias matrix. */
16524	42	double[][] rnpb = jauFw2m(fw.gamb, fw.phib, fw.psib + nut.dpsi, fw.epsa + nut.deps);
16525
16526	42	return rnpb;
16527
16528		}
16529
16530
16531		/**
16532		* Form the matrix of precession/nutation for a given date, IAU 1976
16533		* precession model, IAU 1980 nutation model.
16534		*
16535		*<p>This function is derived from the International Astronomical Union's
16536		* SOFA (Standards Of Fundamental Astronomy) software collection.
16537		*
16538		*<p>Status: support function.
16539		*
16540		*<!-- Given: -->
16541		* @param date1 double TDB date (Note 1)
16542		* @param date2 double TDB date (Note 1)
16543		*
16544		*<!-- Returned: -->
16545		* @return rmatpn double[3][3] <u>returned</u> combined precession/nutation matrix
16546		*
16547		* <p>Notes:
16548		* <ol>
16549		*
16550		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
16551		* convenient way between the two arguments. For example,
16552		* JD(TDB)=2450123.7 could be expressed in any of these ways,
16553		* among others:
16554		*<pre>
16555		* date1 date2
16556		*
16557		* 2450123.7 0.0 (JD method)
16558		* 2451545.0 -1421.3 (J2000 method)
16559		* 2400000.5 50123.2 (MJD method)
16560		* 2450123.5 0.2 (date & time method)
16561		*</pre>
16562		* The JD method is the most natural and convenient to use in
16563		* cases where the loss of several decimal digits of resolution
16564		* is acceptable. The J2000 method is best matched to the way
16565		* the argument is handled internally and will deliver the
16566		* optimum resolution. The MJD method and the date & time methods
16567		* are both good compromises between resolution and convenience.
16568		*
16569		* <li> The matrix operates in the sense V(date) = rmatpn * V(J2000),
16570		* where the p-vector V(date) is with respect to the true equatorial
16571		* triad of date date1+date2 and the p-vector V(J2000) is with
16572		* respect to the mean equatorial triad of epoch J2000.0.
16573		*</ol>
16574		*<p>Called:<ul>
16575		* <li>{@link #jauPmat76} precession matrix, IAU 1976
16576		* <li>{@link #jauNutm80} nutation matrix, IAU 1980
16577		* <li>{@link #jauRxr} product of two r-matrices
16578		* </ul>
16579		*<p>Reference:
16580		*
16581		* <p>Explanatory Supplement to the Astronomical Almanac,
16582		* P. Kenneth Seidelmann (ed), University Science Books (1992),
16583		* Section 3.3 (p145).
16584		*
16585		*@version 2010 January 23
16586		*
16587		* @since Release 20101201
16588		*
16589		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16590		*/
16591		public static double[][] jauPnm80(double date1, double date2)
16592		{
16593	2	double rmatp[][] = new double[3][3], rmatn[][] = new double[3][3];
16594
16595
16596		/* Precession matrix, J2000.0 to date. */
16597	2	rmatp = jauPmat76(date1, date2 );
16598
16599		/* Nutation matrix. */
16600	2	rmatn = jauNutm80(date1, date2);
16601
16602		/* Combine the matrices: PN = N x P. */
16603	2	double[][] rmatpn = jauRxr(rmatn, rmatp);
16604
16605	2	return rmatpn;
16606
16607		}
16608
16609
16610		/**
16611		* Form the matrix of polar motion for a given date, IAU 2000.
16612		*
16613		*<p>This function is derived from the International Astronomical Union's
16614		* SOFA (Standards Of Fundamental Astronomy) software collection.
16615		*
16616		*<p>Status: support function.
16617		*
16618		*<!-- Given: -->
16619		* @param xp double coordinates of the pole (radians, Note 1)
16620		* @param yp double coordinates of the pole (radians, Note 1)
16621		* @param sp double the TIO locator s' (radians, Note 2)
16622		*
16623		*<!-- Returned: -->
16624		* @return double[3][3] <u>returned</u> polar-motion matrix (Note 3)
16625		*
16626		* <p>Notes:
16627		* <ol>
16628		*
16629		* <li> The arguments xp and yp are the coordinates (in radians) of the
16630		* Celestial Intermediate Pole with respect to the International
16631		* Terrestrial Reference System (see IERS Conventions 2003),
16632		* measured along the meridians to 0 and 90 deg west respectively.
16633		*
16634		* <li> The argument sp is the TIO locator s', in radians, which
16635		* positions the Terrestrial Intermediate Origin on the equator. It
16636		* is obtained from polar motion observations by numerical
16637		* integration, and so is in essence unpredictable. However, it is
16638		* dominated by a secular drift of about 47 microarcseconds per
16639		* century, and so can be taken into account by using s' = -47*t,
16640		* where t is centuries since J2000.0. The function jauSp00
16641		* implements this approximation.
16642		*
16643		* <li> The matrix operates in the sense V(TRS) = rpom * V(CIP), meaning
16644		* that it is the final rotation when computing the pointing
16645		* direction to a celestial source.
16646		*</ol>
16647		*<p>Called:<ul>
16648		* <li>{@link #jauIr} initialize r-matrix to identity
16649		* <li>{@link #jauRz} rotate around Z-axis
16650		* <li>{@link #jauRy} rotate around Y-axis
16651		* <li>{@link #jauRx} rotate around X-axis
16652		* </ul>
16653		*<p>Reference:
16654		*
16655		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
16656		* IERS Technical Note No. 32, BKG (2004)
16657		*
16658		*@version 2009 December 17
16659		*
16660		* @since Release 20101201
16661		*
16662		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16663		*/
16664		public static double[][] jauPom00(double xp, double yp, double sp)
16665		{
16666
16667		/* Construct the matrix. */
16668	42	double rpom[][] = new double[3][3];
16669	42	jauIr(rpom);
16670	42	jauRz(sp, rpom);
16671	42	jauRy(-xp, rpom);
16672	42	jauRx(-yp, rpom);
16673
16674	42	return rpom;
16675
16676		}
16677
16678
16679		/**
16680		* P-vector addition.
16681		*
16682		*<p>This function is derived from the International Astronomical Union's
16683		* SOFA (Standards Of Fundamental Astronomy) software collection.
16684		*
16685		*<p>Status: vector/matrix support function.
16686		*
16687		*<!-- Given: -->
16688		* @param a double[3] first p-vector
16689		* @param b double[3] second p-vector
16690		*
16691		*<!-- Returned: -->
16692		* @return apb double[3] <u>returned</u> a + b
16693		*
16694		* Note:
16695		* It is permissible to re-use the same array for any of the
16696		* arguments.
16697		*
16698		*@version 2008 November 18
16699		*
16700		* @since Release 20101201
16701		*
16702		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16703		*/
16704		public static double[] jauPpp(double a[] , double b[] )
16705		{
16706	84	double apb[] = new double[3];
16707	84	apb[0] = a[0] + b[0];
16708	84	apb[1] = a[1] + b[1];
16709	84	apb[2] = a[2] + b[2];
16710
16711	84	return apb;
16712
16713		}
16714
16715
16716		/**
16717		* P-vector plus scaled p-vector.
16718		*
16719		*<p>This function is derived from the International Astronomical Union's
16720		* SOFA (Standards Of Fundamental Astronomy) software collection.
16721		*
16722		*<p>Status: vector/matrix support function.
16723		*
16724		*<!-- Given: -->
16725		* @param a double[3] first p-vector
16726		* @param s double scalar (multiplier for b)
16727		* @param b double[3] second p-vector
16728		*
16729		*<!-- Returned: -->
16730		* @return apsb double[3] <u>returned</u> a + s*b
16731		*
16732		* Note:
16733		* It is permissible for any of a, b and apsb to be the same array.
16734		*
16735		*<p>Called:<ul>
16736		* <li>{@link #jauSxp} multiply p-vector by scalar
16737		* <li>{@link #jauPpp} p-vector plus p-vector
16738		* </ul>
16739		*@version 2008 November 18
16740		*
16741		* @since Release 20101201
16742		*
16743		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16744		*/
16745		static double[] jauPpsp(double a[] , double s, double b[] )
16746		{
16747	54	double sb[] = new double[3], apsb[];
16748
16749
16750		/* sb. /
16751	54	sb = jauSxp(s,b);
16752
16753		/* a + sb. /
16754	54	apsb = jauPpp(a, sb);
16755
16756	54	return apsb;
16757
16758		}
16759
16760		/**
16761		* Precession correction terms.
16762		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
16763		*
16764		* @since AIDA Stage 1
16765		*/
16766		public static class PrecessionDeltaTerms {
16767		/** precession correction in longitude */
16768		public double dpsipr;
16769		/** precession correction in obliquity */
16770		public double depspr;
16771	78	public PrecessionDeltaTerms(double dpsipr, double depspr) {
16772	78	this.dpsipr = dpsipr;
16773	78	this.depspr = depspr;
16774	78	}
16775		}
16776
16777		/**
16778		* Precession-rate part of the IAU 2000 precession-nutation models
16779		* (part of MHB2000).
16780		*
16781		*<p>This function is derived from the International Astronomical Union's
16782		* SOFA (Standards Of Fundamental Astronomy) software collection.
16783		*
16784		*<p>Status: canonical model.
16785		*
16786		*<!-- Given: -->
16787		* @param date1 double TT as a 2-part Julian Date (Note 1)
16788		* @param date2 double TT as a 2-part Julian Date (Note 1)
16789		*
16790		*<!-- Returned: -->
16791		* @param dpsipr double <u>returned</u> precession corrections (Notes 2,3)
16792		* @param depspr double <u>returned</u> precession corrections (Notes 2,3)
16793		*
16794		* <p>Notes:
16795		* <ol>
16796		*
16797		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
16798		* convenient way between the two arguments. For example,
16799		* JD(TT)=2450123.7 could be expressed in any of these ways,
16800		* among others:
16801		*<pre>
16802		* date1 date2
16803		*
16804		* 2450123.7 0.0 (JD method)
16805		* 2451545.0 -1421.3 (J2000 method)
16806		* 2400000.5 50123.2 (MJD method)
16807		* 2450123.5 0.2 (date & time method)
16808		*</pre>
16809		* The JD method is the most natural and convenient to use in
16810		* cases where the loss of several decimal digits of resolution
16811		* is acceptable. The J2000 method is best matched to the way
16812		* the argument is handled internally and will deliver the
16813		* optimum resolution. The MJD method and the date & time methods
16814		* are both good compromises between resolution and convenience.
16815		*
16816		* <li> The precession adjustments are expressed as "nutation
16817		* components", corrections in longitude and obliquity with respect
16818		* to the J2000.0 equinox and ecliptic.
16819		*
16820		* <li> Although the precession adjustments are stated to be with respect
16821		* to Lieske et al. (1977), the MHB2000 model does not specify which
16822		* set of Euler angles are to be used and how the adjustments are to
16823		* be applied. The most literal and straightforward procedure is to
16824		* adopt the 4-rotation epsilon_0, psi_A, omega_A, xi_A option, and
16825		* to add dpsipr to psi_A and depspr to both omega_A and eps_A.
16826		*
16827		* <li> This is an implementation of one aspect of the IAU 2000A nutation
16828		* model, formally adopted by the IAU General Assembly in 2000,
16829		* namely MHB2000 (Mathews et al. 2002).
16830		*
16831		*<p>References:
16832		*
16833		* <p>Lieske, J.H., Lederle, T., Fricke, W. & Morando, B., "Expressions
16834		* for the precession quantities based upon the IAU (1976) System of
16835		* Astronomical Constants", Astron.Astrophys., 58, 1-16 (1977)
16836		*
16837		* <p>Mathews, P.M., Herring, T.A., Buffet, B.A., "Modeling of nutation
16838		* and precession New nutation series for nonrigid Earth and
16839		* insights into the Earth's interior", J.Geophys.Res., 107, B4,
16840		* 2002. The MHB2000 code itself was obtained on 9th September 2002
16841		* from ftp://maia.usno.navy.mil/conv2000/chapter5/IAU2000A.
16842		*
16843		* <p>Wallace, P.T., "Software for Implementing the IAU 2000
16844		* Resolutions", in IERS Workshop 5.1 (2002).
16845		*
16846		*@version 2009 December 17
16847		*
16848		* @since Release 20101201
16849		*
16850		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16851		*/
16852		static PrecessionDeltaTerms jauPr00(double date1, double date2)
16853		{
16854		double t;
16855
16856		/* Precession and obliquity corrections (radians per century) */
16857	78	final double PRECOR = -0.29965 * DAS2R,
16858	78	OBLCOR = -0.02524 * DAS2R;
16859
16860
16861		/* Interval between fundamental epoch J2000.0 and given date (JC). */
16862	78	t = ((date1 - DJ00) + date2) / DJC;
16863
16864		/* Precession rate contributions with respect to IAU 1976/80. */
16865	78	double dpsipr = PRECOR * t;
16866	78	double depspr = OBLCOR * t;
16867
16868	78	return new PrecessionDeltaTerms(dpsipr, depspr);
16869
16870		}
16871
16872		/**
16873		* Euler Angles.
16874		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
16875		*
16876		* @since AIDA Stage 1
16877		*/
16878		public static class EulerAngles {
16879		/** 1st rotation: radians cw around z */
16880		public double zeta;
16881		/** 3rd rotation: radians cw around z */
16882		public double z;
16883		/** 2nd rotation: radians ccw around y */
16884		public double theta;
16885	8	public EulerAngles(double zeta, double z, double theta){
16886	8	this.zeta = zeta;
16887	8	this.z = z;
16888	8	this.theta = theta;
16889	8	}
16890		}
16891
16892		/**
16893		* IAU 1976 precession model.
16894		*
16895		* This function forms the three Euler angles which implement general
16896		* precession between two epochs, using the IAU 1976 model (as for
16897		* the FK5 catalog).
16898		*
16899		*<p>This function is derived from the International Astronomical Union's
16900		* SOFA (Standards Of Fundamental Astronomy) software collection.
16901		*
16902		*<p>Status: canonical model.
16903		*
16904		*<!-- Given: -->
16905		* @param ep01 double TDB starting epoch (Note 1)
16906		* @param ep02 double TDB starting epoch (Note 1)
16907		* @param ep11 double TDB ending epoch (Note 1)
16908		* @param ep12 double TDB ending epoch (Note 1)
16909		*
16910		*<!-- Returned: -->
16911		* @param zeta double <u>returned</u> 1st rotation: radians cw around z
16912		* @param z double <u>returned</u> 3rd rotation: radians cw around z
16913		* @param theta double <u>returned</u> 2nd rotation: radians ccw around y
16914		*
16915		* <p>Notes:
16916		* <ol>
16917		*
16918		* <li> The epochs ep01+ep02 and ep11+ep12 are Julian Dates, apportioned
16919		* in any convenient way between the arguments epn1 and epn2. For
16920		* example, JD(TDB)=2450123.7 could be expressed in any of these
16921		* ways, among others:
16922		*
16923		* epn1 epn2
16924		*
16925		* 2450123.7 0.0 (JD method)
16926		* 2451545.0 -1421.3 (J2000 method)
16927		* 2400000.5 50123.2 (MJD method)
16928		* 2450123.5 0.2 (date & time method)
16929		*</pre>
16930		* The JD method is the most natural and convenient to use in cases
16931		* where the loss of several decimal digits of resolution is
16932		* acceptable. The J2000 method is best matched to the way the
16933		* argument is handled internally and will deliver the optimum
16934		* optimum resolution. The MJD method and the date & time methods
16935		* are both good compromises between resolution and convenience.
16936		* The two epochs may be expressed using different methods, but at
16937		* the risk of losing some resolution.
16938		*
16939		* <li> The accumulated precession angles zeta, z, theta are expressed
16940		* through canonical polynomials which are valid only for a limited
16941		* time span. In addition, the IAU 1976 precession rate is known to
16942		* be imperfect. The absolute accuracy of the present formulation
16943		* is better than 0.1 arcsec from 1960AD to 2040AD, better than
16944		* 1 arcsec from 1640AD to 2360AD, and remains below 3 arcsec for
16945		* the whole of the period 500BC to 3000AD. The errors exceed
16946		* 10 arcsec outside the range 1200BC to 3900AD, exceed 100 arcsec
16947		* outside 4200BC to 5600AD and exceed 1000 arcsec outside 6800BC to
16948		* 8200AD.
16949		*
16950		* <li> The three angles are returned in the conventional order, which
16951		* is not the same as the order of the corresponding Euler
16952		* rotations. The precession matrix is
16953		* R_3(-z) x R_2(+theta) x R_3(-zeta).
16954		*
16955		*<p>Reference:
16956		*
16957		* <p>Lieske, J.H., 1979, Astron.Astrophys. 73, 282, equations
16958		* (6) & (7), p283.
16959		*
16960		*@version 2009 December 17
16961		*
16962		* @since Release 20101201
16963		*
16964		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
16965		*/
16966		static EulerAngles jauPrec76(double ep01, double ep02, double ep11, double ep12)
16967		{
16968		double t0, t, tas2r, w;
16969
16970
16971		/* Interval between fundamental epoch J2000.0 and start epoch (JC). */
16972	6	t0 = ((ep01 - DJ00) + ep02) / DJC;
16973
16974		/* Interval over which precession required (JC). */
16975	6	t = ((ep11 - ep01) + (ep12 - ep02)) / DJC;
16976
16977		/* Euler angles. */
16978	6	tas2r = t * DAS2R;
16979	6	w = 2306.2181 + (1.39656 - 0.000139 * t0) * t0;
16980
16981	6	double zeta = (w + ((0.30188 - 0.000344 * t0) + 0.017998 * t) * t) * tas2r;
16982
16983	6	double z = (w + ((1.09468 + 0.000066 * t0) + 0.018203 * t) * t) * tas2r;
16984
16985	6	double theta = ((2004.3109 + (-0.85330 - 0.000217 * t0) * t0)
16986		+ ((-0.42665 - 0.000217 * t0) - 0.041833 * t) * t) * tas2r;
16987
16988	6	return new EulerAngles(zeta, z, theta);
16989
16990		}
16991
16992
16993		/**
16994		* Discard velocity component of a pv-vector.
16995		*
16996		*<p>This function is derived from the International Astronomical Union's
16997		* SOFA (Standards Of Fundamental Astronomy) software collection.
16998		*
16999		*<p>Status: vector/matrix support function.
17000		*
17001		*<!-- Given: -->
17002		* @param pv double[2][3] pv-vector
17003		*
17004		*<!-- Returned: -->
17005		* @return p double[3] <u>returned</u> p-vector
17006		*
17007		*<p>Called:<ul>
17008		* <li>{@link #jauCp} copy p-vector
17009		* </ul>
17010		*@version 2008 May 11
17011		*
17012		* @since Release 20101201
17013		*
17014		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17015		*/
17016		public static double[] jauPv2p(double pv[][] )
17017		{
17018	2	double p[] = new double[3];
17019	2	jauCp(pv[0], p);
17020
17021	2	return p;
17022
17023		}
17024
17025
17026		/**
17027		* A position and velocity expressed in spherical polar coordinates.
17028		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
17029		*
17030		* @since AIDA Stage 1
17031		*/
17032		public static class SphericalPositionVelocity {
17033		public SphericalPosition pos;
17034		public SphericalPosition vel;
17035		public SphericalPositionVelocity( double theta, double phi, double r,
17036	14	double td, double pd, double rd) {
17037	14	pos = new SphericalPosition(theta, phi, r);
17038	14	vel = new SphericalPosition(td,pd,rd);
17039	14	}
17040		}
17041		/**
17042		* Convert position/velocity from Cartesian to spherical coordinates.
17043		*
17044		*<p>This function is derived from the International Astronomical Union's
17045		* SOFA (Standards Of Fundamental Astronomy) software collection.
17046		*
17047		*<p>Status: vector/matrix support function.
17048		*
17049		*<!-- Given: -->
17050		* @param pv double[2][3] pv-vector
17051		*
17052		*<!-- Returned: -->
17053		* @return theta double <u>returned</u> longitude angle (radians)
17054		* phi double <u>returned</u> latitude angle (radians)
17055		* r double <u>returned</u> radial distance
17056		* td double <u>returned</u> rate of change of theta
17057		* pd double <u>returned</u> rate of change of phi
17058		* rd double <u>returned</u> rate of change of r
17059		*
17060		* <p>Notes:
17061		* <ol>
17062		*
17063		* <li> If the position part of pv is null, theta, phi, td and pd
17064		* are indeterminate. This is handled by extrapolating the
17065		* position through unit time by using the velocity part of
17066		* pv. This moves the origin without changing the direction
17067		* of the velocity component. If the position and velocity
17068		* components of pv are both null, zeroes are returned for all
17069		* six results.
17070		*
17071		* <li> If the position is a pole, theta, td and pd are indeterminate.
17072		* In such cases zeroes are returned for all three.
17073		*</ol>
17074		*@version 2008 October 28
17075		*
17076		* @since Release 20101201
17077		*
17078		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17079		*/
17080		public static SphericalPositionVelocity jauPv2s(double pv[][])
17081		{
17082		double x, y, z, xd, yd, zd, rxy2, rxy, r2, rtrue, rw, xyp;
17083		double theta, phi, r, td, pd, rd;
17084
17085		/* Components of position/velocity vector. */
17086	14	x = pv[0][0];
17087	14	y = pv[0][1];
17088	14	z = pv[0][2];
17089	14	xd = pv[1][0];
17090	14	yd = pv[1][1];
17091	14	zd = pv[1][2];
17092
17093		/* Component of r in XY plane squared. */
17094	14	rxy2 = xx + yy;
17095
17096		/* Modulus squared. */
17097	14	r2 = rxy2 + z*z;
17098
17099		/* Modulus. */
17100	14	rtrue = sqrt(r2);
17101
17102		/* If null vector, move the origin along the direction of movement. */
17103	14	rw = rtrue;
17104	14	if (rtrue == 0.0) {
17105	0	x = xd;
17106	0	y = yd;
17107	0	z = zd;
17108	0	rxy2 = xx + yy;
17109	0	r2 = rxy2 + z*z;
17110	0	rw = sqrt(r2);
17111		}
17112
17113		/* Position and velocity in spherical coordinates. */
17114	14	rxy = sqrt(rxy2);
17115	14	xyp = xxd + yyd;
17116	14	if (rxy2 != 0.0) {
17117	14	theta = atan2(y, x);
17118	14	phi = atan2(z, rxy);
17119	14	td = (xyd - yxd) / rxy2;
17120	14	pd = (zdrxy2 - zxyp) / (r2*rxy);
17121		} else {
17122	0	theta = 0.0;
17123	0	phi = (z != 0.0) ? atan2(z, rxy) : 0.0;
17124	0	td = 0.0;
17125	0	pd = 0.0;
17126		}
17127	14	r = rtrue;
17128	14	rd = (rw != 0.0) ? (xyp + z*zd) / rw : 0.0;
17129
17130	14	return new SphericalPositionVelocity(theta, phi, r, td, pd, rd);
17131
17132		}
17133
17134
17135		/**
17136		* Inner (=scalar=dot) product of two pv-vectors.
17137		*
17138		*<p>This function is derived from the International Astronomical Union's
17139		* SOFA (Standards Of Fundamental Astronomy) software collection.
17140		*
17141		*<p>Status: vector/matrix support function.
17142		*
17143		*<!-- Given: -->
17144		* @param a double[2][3] first pv-vector
17145		* @param b double[2][3] second pv-vector
17146		*
17147		*<!-- Returned: -->
17148		* @return adb double[2] <u>returned</u> a . b (see note)
17149		*
17150		* Note:
17151		*
17152		* If the position and velocity components of the two pv-vectors are
17153		* ( ap, av ) and ( bp, bv ), the result, a . b, is the pair of
17154		* numbers ( ap . bp , ap . bv + av . bp ). The two numbers are the
17155		* dot-product of the two p-vectors and its derivative.
17156		*
17157		*<p>Called:<ul>
17158		* <li>{@link #jauPdp} scalar product of two p-vectors
17159		* </ul>
17160		*@version 2008 May 22
17161		*
17162		* @since Release 20101201
17163		*
17164		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17165		*/
17166		public static double[] jauPvdpv(double a[][], double b[][] )
17167		{
17168	2	double adbd, addb, adb[] = new double[2];
17169
17170
17171		/* a . b = constant part of result. */
17172	2	adb[0] = jauPdp(a[0], b[0]);
17173
17174		/* a . bdot */
17175	2	adbd = jauPdp(a[0], b[1]);
17176
17177		/* adot . b */
17178	2	addb = jauPdp(a[1], b[0]);
17179
17180		/* Velocity part of result. */
17181	2	adb[1] = adbd + addb;
17182
17183	2	return adb;
17184
17185		}
17186
17187
17188		/**
17189		* Modulus of pv-vector.
17190		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
17191		*
17192		* @since AIDA Stage 1
17193		*/
17194		public static class PVModulus{
17195		public double r;
17196		public double s;
17197	2	public PVModulus( double r, double s){
17198	2	this.r = r;
17199	2	this.s = s;
17200	2	}
17201		}
17202		/**
17203		* Modulus of pv-vector.
17204		*
17205		*<p>This function is derived from the International Astronomical Union's
17206		* SOFA (Standards Of Fundamental Astronomy) software collection.
17207		*
17208		*<p>Status: vector/matrix support function.
17209		*
17210		*<!-- Given: -->
17211		* @param pv double[2][3] pv-vector
17212		*
17213		*<!-- Returned: -->
17214		* @return modulus of position component,
17215		* modulus of velocity component
17216		*
17217		*<p>Called:<ul>
17218		* <li>{@link #jauPm} modulus of p-vector
17219		* </ul>
17220		*@version 2008 May 22
17221		*
17222		* @since Release 20101201
17223		*
17224		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17225		*/
17226		public static PVModulus jauPvm(double pv[][])
17227		{
17228		/* Distance. */
17229	2	double r = jauPm(pv[0]);
17230
17231		/* Speed. */
17232	2	double s = jauPm(pv[1]);
17233
17234	2	return new PVModulus(r, s);
17235
17236		}
17237
17238
17239		/**
17240		* Subtract one pv-vector from another.
17241		*
17242		*<p>This function is derived from the International Astronomical Union's
17243		* SOFA (Standards Of Fundamental Astronomy) software collection.
17244		*
17245		*<p>Status: vector/matrix support function.
17246		*
17247		*<!-- Given: -->
17248		* @param a double[2][3] first pv-vector
17249		* @param b double[2][3] second pv-vector
17250		*
17251		*<!-- Returned: -->
17252		* @return double[2][3] <u>returned</u> a - b
17253		*
17254		* Note:
17255		* It is permissible to re-use the same array for any of the
17256		* arguments.
17257		*
17258		*<p>Called:<ul>
17259		* <li>{@link #jauPmp} p-vector minus p-vector
17260		* </ul>
17261		*@version 2008 November 18
17262		*
17263		* @since Release 20101201
17264		*
17265		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17266		*/
17267		public static double[][] jauPvmpv(double a[][], double b[][])
17268		{
17269	2	double amb[][] = new double[2][3];
17270	2	amb[0] = jauPmp(a[0], b[0]);
17271	2	amb[1] = jauPmp(a[1], b[1]);
17272
17273	2	return amb;
17274
17275		}
17276
17277
17278		/**
17279		* Add one pv-vector to another.
17280		*
17281		*<p>This function is derived from the International Astronomical Union's
17282		* SOFA (Standards Of Fundamental Astronomy) software collection.
17283		*
17284		*<p>Status: vector/matrix support function.
17285		*
17286		*<!-- Given: -->
17287		* @param a double[2][3] first pv-vector
17288		* @param b double[2][3] second pv-vector
17289		*
17290		*<!-- Returned: -->
17291		* @return apb double[2][3] <u>returned</u> a + b
17292		*
17293		* Note:
17294		* It is permissible to re-use the same array for any of the
17295		* arguments.
17296		*
17297		*<p>Called:<ul>
17298		* <li>{@link #jauPpp} p-vector plus p-vector
17299		* </ul>
17300		*@version 2008 November 18
17301		*
17302		* @since Release 20101201
17303		*
17304		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17305		*/
17306		public static double[][] jauPvppv(double a[][], double b[][])
17307		{
17308	2	double apb[][] = new double[2][3];
17309	2	apb[0] = jauPpp(a[0], b[0]);
17310	2	apb[1] = jauPpp(a[1], b[1]);
17311
17312	2	return apb;
17313
17314		}
17315
17316
17317		/**
17318		* Typical catalogue coordinates. i.e. Position, proper motion, parallax and radial velocity.
17319		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 4 Feb 2010
17320		*
17321		* @since AIDA Stage 1
17322		*/
17323		public static class CatalogCoords {
17324		/** position (radians) */
17325		public SphericalCoordinate pos;
17326		/** proper motion (radians/year)*/
17327		public SphericalCoordinate pm;
17328		/** parallax (arcsec) */
17329		public double px;
17330		/** radial velocity (km/s, positive = receding) */
17331		public double rv;
17332
17333		public CatalogCoords(double ra, double dec,
17334	12	double pmr, double pmd, double px, double rv) {
17335	12	this.pos = new SphericalCoordinate(ra, dec);
17336	12	this.pm = new SphericalCoordinate(pmr, pmd);
17337	12	this.px = px;
17338	12	this.rv = rv;
17339	12	}
17340		}
17341		/**
17342		* Convert star position+velocity vector to catalog coordinates.
17343		*
17344		*<p>This function is derived from the International Astronomical Union's
17345		* SOFA (Standards Of Fundamental Astronomy) software collection.
17346		*
17347		*<p>Status: support function.
17348		*
17349		* Given (Note 1):
17350		* pv double[2][3] pv-vector (AU, AU/day)
17351		*
17352		* Returned (Note 2):
17353		* ra double right ascension (radians)
17354		* dec double declination (radians)
17355		* pmr double RA proper motion (radians/year)
17356		* pmd double Dec proper motion (radians/year)
17357		* px double parallax (arcsec)
17358		* rv double radial velocity (km/s, positive = receding)
17359		*
17360		* <!-- Returned (function value): -->
17361		* @return int status:
17362		* 0 = OK
17363		* -1 = superluminal speed (Note 5)
17364		* -2 = null position vector
17365		*
17366		* <p>Notes:
17367		* <ol>
17368		*
17369		* <li> The specified pv-vector is the coordinate direction (and its rate
17370		* of change) for the date at which the light leaving the star
17371		* reached the solar-system barycenter.
17372		*
17373		* <li> The star data returned by this function are "observables" for an
17374		* imaginary observer at the solar-system barycenter. Proper motion
17375		* and radial velocity are, strictly, in terms of barycentric
17376		* coordinate time, TCB. For most practical applications, it is
17377		* permissible to neglect the distinction between TCB and ordinary
17378		* "proper" time on Earth (TT/TAI). The result will, as a rule, be
17379		* limited by the intrinsic accuracy of the proper-motion and
17380		* radial-velocity data; moreover, the supplied pv-vector is likely
17381		* to be merely an intermediate result (for example generated by the
17382		* function jauStarpv), so that a change of time unit will cancel
17383		* out overall.
17384		*
17385		* In accordance with normal star-catalog conventions, the object's
17386		* right ascension and declination are freed from the effects of
17387		* secular aberration. The frame, which is aligned to the catalog
17388		* equator and equinox, is Lorentzian and centered on the SSB.
17389		*
17390		* Summarizing, the specified pv-vector is for most stars almost
17391		* identical to the result of applying the standard geometrical
17392		* "space motion" transformation to the catalog data. The
17393		* differences, which are the subject of the Stumpff paper cited
17394		* below, are:
17395		*
17396		* (i) In stars with significant radial velocity and proper motion,
17397		* the constantly changing light-time distorts the apparent proper
17398		* motion. Note that this is a classical, not a relativistic,
17399		* effect.
17400		*
17401		* (ii) The transformation complies with special relativity.
17402		*
17403		* <li> Care is needed with units. The star coordinates are in radians
17404		* and the proper motions in radians per Julian year, but the
17405		* parallax is in arcseconds; the radial velocity is in km/s, but
17406		* the pv-vector result is in AU and AU/day.
17407		*
17408		* <li> The proper motions are the rate of change of the right ascension
17409		* and declination at the catalog epoch and are in radians per Julian
17410		* year. The RA proper motion is in terms of coordinate angle, not
17411		* true angle, and will thus be numerically larger at high
17412		* declinations.
17413		*
17414		* <li> Straight-line motion at constant speed in the inertial frame is
17415		* assumed. If the speed is greater than or equal to the speed of
17416		* light, the function aborts with an error status.
17417		*
17418		* <li> The inverse transformation is performed by the function jauStarpv.
17419		*</ol>
17420		*<p>Called:<ul>
17421		* <li>{@link #jauPn} decompose p-vector into modulus and direction
17422		* <li>{@link #jauPdp} scalar product of two p-vectors
17423		* <li>{@link #jauSxp} multiply p-vector by scalar
17424		* <li>{@link #jauPmp} p-vector minus p-vector
17425		* <li>{@link #jauPm} modulus of p-vector
17426		* <li>{@link #jauPpp} p-vector plus p-vector
17427		* <li>{@link #jauPv2s} pv-vector to spherical
17428		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
17429		* </ul>
17430		*<p>Reference:
17431		*
17432		* Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
17433		*
17434		*@version 2008 May 18
17435		*
17436		* @since Release 20101201
17437		*
17438		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17439		*/
17440		public static CatalogCoords jauPvstar(double pv[][]) throws JSOFAInternalError
17441		{
17442	10	double x[] = new double[3], vr, ur[] = new double[3], vt, ut[] = new double[3], bett, betr, d, w, del,
17443	10	usr[] = new double[3], ust[] = new double[3];
17444
17445
17446		/* Isolate the radial component of the velocity (AU/day, inertial). */
17447	10	NormalizedVector nv = jauPn(pv[0]);
17448	10	x = nv.u;
17449	10	vr = jauPdp(x, pv[1]);
17450	10	ur = jauSxp(vr,x);
17451
17452		/* Isolate the transverse component of the velocity (AU/day, inertial). */
17453	10	ut = jauPmp(pv[1], ur);
17454	10	vt = jauPm(ut);
17455
17456		/* Special-relativity dimensionless parameters. */
17457	10	bett = vt / DC;
17458	10	betr = vr / DC;
17459
17460		/* The inertial-to-observed correction terms. */
17461	10	d = 1.0 + betr;
17462	10	w = 1.0 - betrbetr - bettbett;
17463	10	if (d == 0.0 \|\| w < 0) throw new JSOFAInternalError("Superluminal speed", -1);
17464	10	del = sqrt(w) - 1.0;
17465
17466		/* Apply relativistic correction factor to radial velocity component. */
17467	10	w = (betr != 0) ? (betr - del) / (betr * d) : 1.0;
17468	10	usr = jauSxp(w,ur);
17469
17470		/* Apply relativistic correction factor to tangential velocity */
17471		/* component. */
17472	10	ust = jauSxp(1.0/d, ut);
17473
17474		/* Combine the two to obtain the observed velocity vector (AU/day). */
17475	10	pv[1] = jauPpp(usr, ust);
17476
17477		/* Cartesian to spherical. */
17478	10	SphericalPositionVelocity pvs = jauPv2s(pv);
17479	10	if (pvs.pos.r == 0.0) throw new JSOFAInternalError("null position vector", -2);
17480
17481		/* Return RA in range 0 to 2pi. */
17482	10	double ra = jauAnp(pvs.pos.theta);
17483
17484		/* Return proper motions in radians per year. */
17485	10	double pmr = pvs.vel.theta * DJY;
17486	10	double pmd = pvs.vel.phi * DJY;
17487
17488		/* Return parallax in arcsec. */
17489	10	double px = DR2AS / pvs.pos.r;
17490
17491		/* Return radial velocity in km/s. */
17492	10	double rv = 1e-3 * pvs.vel.r * DAU / DAYSEC;
17493
17494		/* OK status. */
17495	10	return new CatalogCoords(ra, pvs.pos.phi, pmr, pmd, px, rv);
17496
17497		}
17498
17499
17500		/**
17501		* Update a pv-vector.
17502		*
17503		*<p>This function is derived from the International Astronomical Union's
17504		* SOFA (Standards Of Fundamental Astronomy) software collection.
17505		*
17506		*<p>Status: vector/matrix support function.
17507		*
17508		*<!-- Given: -->
17509		* @param dt double time interval
17510		* @param pv double[2][3] pv-vector
17511		*
17512		*<!-- Returned: -->
17513		* @return upv double[2][3] <u>returned</u> p updated, v unchanged
17514		*
17515		* <p>Notes:
17516		* <ol>
17517		*
17518		* <li> "Update" means "refer the position component of the vector
17519		* to a new date dt time units from the existing date".
17520		*
17521		* <li> The time units of dt must match those of the velocity.
17522		*
17523		* <li> It is permissible for pv and upv to be the same array.
17524		*</ol>
17525		*<p>Called:<ul>
17526		* <li>{@link #jauPpsp} p-vector plus scaled p-vector
17527		* <li>{@link #jauCp} copy p-vector
17528		* </ul>
17529		*@version 2008 November 17
17530		*
17531		* @since Release 20101201
17532		*
17533		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17534		*/
17535		public static double[][] jauPvu(double dt, double pv[][] )
17536		{
17537	10	double upv[][] = new double[2][3];
17538	10	upv[0] = jauPpsp(pv[0], dt, pv[1]);
17539	10	jauCp(pv[1], upv[1]);
17540
17541	10	return upv;
17542
17543		}
17544
17545
17546		/**
17547		* Update a pv-vector, discarding the velocity component.
17548		*
17549		*<p>This function is derived from the International Astronomical Union's
17550		* SOFA (Standards Of Fundamental Astronomy) software collection.
17551		*
17552		*<p>Status: vector/matrix support function.
17553		*
17554		*<!-- Given: -->
17555		* @param dt double time interval
17556		* @param pv double[2][3] pv-vector
17557		*
17558		*<!-- Returned: -->
17559		* @return p double[3] <u>returned</u> p-vector
17560		*
17561		* <p>Notes:
17562		* <ol>
17563		*
17564		* <li> "Update" means "refer the position component of the vector to a
17565		* new date dt time units from the existing date".
17566		*
17567		* <li> The time units of dt must match those of the velocity.
17568		*</ol>
17569		*@version 2008 May 11
17570		*
17571		* @since Release 20101201
17572		*
17573		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17574		*/
17575		public static double[] jauPvup(double dt, double pv[][] )
17576		{
17577	2	double p[] = new double[3];
17578	2	p[0] = pv[0][0] + dt * pv[1][0];
17579	2	p[1] = pv[0][1] + dt * pv[1][1];
17580	2	p[2] = pv[0][2] + dt * pv[1][2];
17581
17582	2	return p;
17583
17584		}
17585
17586
17587		/**
17588		* Outer (=vector=cross) product of two pv-vectors.
17589		*
17590		*<p>This function is derived from the International Astronomical Union's
17591		* SOFA (Standards Of Fundamental Astronomy) software collection.
17592		*
17593		*<p>Status: vector/matrix support function.
17594		*
17595		*<!-- Given: -->
17596		* @param a double[2][3] first pv-vector
17597		* @param b double[2][3] second pv-vector
17598		*
17599		*<!-- Returned: -->
17600		* @return axb double[2][3] <u>returned</u> a x b
17601		*
17602		* <p>Notes:
17603		* <ol>
17604		*
17605		* <li> If the position and velocity components of the two pv-vectors are
17606		* ( ap, av ) and ( bp, bv ), the result, a x b, is the pair of
17607		* vectors ( ap x bp, ap x bv + av x bp ). The two vectors are the
17608		* cross-product of the two p-vectors and its derivative.
17609		*
17610		* <li> It is permissible to re-use the same array for any of the
17611		* arguments.
17612		*</ol>
17613		*<p>Called:<ul>
17614		* <li>{@link #jauCpv} copy pv-vector
17615		* <li>{@link #jauPxp} vector product of two p-vectors
17616		* <li>{@link #jauPpp} p-vector plus p-vector
17617		* </ul>
17618		*@version 2008 November 18
17619		*
17620		* @since Release 20101201
17621		*
17622		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17623		*/
17624		public static double[][] jauPvxpv(double a[][], double b[][] )
17625		{
17626	2	double wa[][] = new double[2][3], wb[][] = new double[2][3], axbd[] = new double[3], adxb[] = new double[3];
17627
17628	2	double axb[][] = new double[2][3];
17629		/* Make copies of the inputs. */
17630	2	jauCpv(a, wa);
17631	2	jauCpv(b, wb);
17632
17633		/* a x b = position part of result. */
17634	2	axb[0] = jauPxp(wa[0], wb[0]);
17635
17636		/* a x bdot + adot x b = velocity part of result. */
17637	2	axbd = jauPxp(wa[0],wb[1]);
17638	2	adxb = jauPxp(wa[1],wb[0]);
17639	2	axb[1] = jauPpp(axbd, adxb);
17640
17641	2	return axb;
17642
17643		}
17644
17645
17646		/**
17647		* p-vector outer (=vector=cross) product.
17648		*
17649		*<p>This function is derived from the International Astronomical Union's
17650		* SOFA (Standards Of Fundamental Astronomy) software collection.
17651		*
17652		*<p>Status: vector/matrix support function.
17653		*
17654		*<!-- Given: -->
17655		* @param a double[3] first p-vector
17656		* @param b double[3] second p-vector
17657		*
17658		*<!-- Returned: -->
17659		* @return axb double[3] <u>returned</u> a x b
17660		*
17661		* Note:
17662		* It is permissible to re-use the same array for any of the
17663		* arguments.
17664		*
17665		*@version 2008 November 18
17666		*
17667		* @since Release 20101201
17668		*
17669		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17670		*/
17671		public static double[] jauPxp(double a[] , double b[] )
17672		{
17673		double xa, ya, za, xb, yb, zb;
17674	250	double axb[] = new double[3];
17675
17676	250	xa = a[0];
17677	250	ya = a[1];
17678	250	za = a[2];
17679	250	xb = b[0];
17680	250	yb = b[1];
17681	250	zb = b[2];
17682	250	axb[0] = yazb - zayb;
17683	250	axb[1] = zaxb - xazb;
17684	250	axb[2] = xayb - yaxb;
17685
17686	250	return axb;
17687
17688		}
17689
17690
17691		/**
17692		* Express an r-matrix as an r-vector.
17693		*
17694		*<p>This function is derived from the International Astronomical Union's
17695		* SOFA (Standards Of Fundamental Astronomy) software collection.
17696		*
17697		*<p>Status: vector/matrix support function.
17698		*
17699		*<!-- Given: -->
17700		* @param r double[3][3] rotation matrix
17701		*
17702		*<!-- Returned: -->
17703		* @return w double[3] <u>returned</u> rotation vector (Note 1)
17704		*
17705		* <p>Notes:
17706		* <ol>
17707		*
17708		* <li> A rotation matrix describes a rotation through some angle about
17709		* some arbitrary axis called the Euler axis. The "rotation vector"
17710		* returned by this function has the same direction as the Euler axis,
17711		* and its magnitude is the angle in radians. (The magnitude and
17712		* direction can be separated by means of the function jauPn.)
17713		*
17714		* <li> If r is null, so is the result. If r is not a rotation matrix
17715		* the result is undefined; r must be proper (i.e. have a positive
17716		* determinant) and real orthogonal (inverse = transpose).
17717		*
17718		* <li> The reference frame rotates clockwise as seen looking along
17719		* the rotation vector from the origin.
17720		*</ol>
17721		*@version 2008 May 12
17722		*
17723		* @since Release 20101201
17724		*
17725		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17726		*/
17727		public static double[] jauRm2v(double r[][] )
17728		{
17729		double x, y, z, s2, c2, phi, f;
17730	2	double w[] = new double[3];
17731
17732	2	x = r[1][2] - r[2][1];
17733	2	y = r[2][0] - r[0][2];
17734	2	z = r[0][1] - r[1][0];
17735	2	s2 = sqrt(xx + yy + z*z);
17736	2	if (s2 > 0) {
17737	2	c2 = r[0][0] + r[1][1] + r[2][2] - 1;
17738	2	phi = atan2(s2, c2);
17739	2	f = phi / s2;
17740	2	w[0] = x * f;
17741	2	w[1] = y * f;
17742	2	w[2] = z * f;
17743		} else {
17744	0	w[0] = 0.0;
17745	0	w[1] = 0.0;
17746	0	w[2] = 0.0;
17747		}
17748
17749	2	return w;
17750
17751		}
17752
17753
17754		/**
17755		* Form the r-matrix corresponding to a given r-vector.
17756		*
17757		*<p>This function is derived from the International Astronomical Union's
17758		* SOFA (Standards Of Fundamental Astronomy) software collection.
17759		*
17760		*<p>Status: vector/matrix support function.
17761		*
17762		*<!-- Given: -->
17763		* @param w double[3] rotation vector (Note 1)
17764		*
17765		*<!-- Returned: -->
17766		* @return r double[3][3] <u>returned</u> rotation matrix
17767		*
17768		* <p>Notes:
17769		* <ol>
17770		*
17771		* <li> A rotation matrix describes a rotation through some angle about
17772		* some arbitrary axis called the Euler axis. The "rotation vector"
17773		* supplied to This function has the same direction as the Euler
17774		* axis, and its magnitude is the angle in radians.
17775		*
17776		* <li> If w is null, the unit matrix is returned.
17777		*
17778		* <li> The reference frame rotates clockwise as seen looking along the
17779		* rotation vector from the origin.
17780		*</ol>
17781		*@version 2008 May 11
17782		*
17783		* @since Release 20101201
17784		*
17785		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17786		*/
17787		public static double[][] jauRv2m(double w[])
17788		{
17789		double x, y, z, phi, s, c, f;
17790	16	double r[][] = new double[3][3];
17791
17792
17793		/* Euler angle (magnitude of rotation vector) and functions. */
17794	16	x = w[0];
17795	16	y = w[1];
17796	16	z = w[2];
17797	16	phi = sqrt(xx + yy + z*z);
17798	16	s = sin(phi);
17799	16	c = cos(phi);
17800	16	f = 1.0 - c;
17801
17802		/* Euler axis (direction of rotation vector), perhaps null. */
17803	16	if (phi > 0.0) {
17804	16	x /= phi;
17805	16	y /= phi;
17806	16	z /= phi;
17807		}
17808
17809		/* Form the rotation matrix. */
17810	16	r[0][0] = xxf + c;
17811	16	r[0][1] = xyf + z*s;
17812	16	r[0][2] = xzf - y*s;
17813	16	r[1][0] = yxf - z*s;
17814	16	r[1][1] = yyf + c;
17815	16	r[1][2] = yzf + x*s;
17816	16	r[2][0] = zxf + y*s;
17817	16	r[2][1] = zyf - x*s;
17818	16	r[2][2] = zzf + c;
17819
17820	16	return r;
17821
17822		}
17823
17824
17825		/**
17826		* Rotate an r-matrix about the x-axis.
17827		*
17828		*<p>This function is derived from the International Astronomical Union's
17829		* SOFA (Standards Of Fundamental Astronomy) software collection.
17830		*
17831		*<p>Status: vector/matrix support function.
17832		*
17833		*<!-- Given: -->
17834		* @param phi double angle (radians)
17835		*
17836		* Given and returned:
17837		* @param r double[3][3] r-matrix <u>given and returned</u>
17838		*
17839		* Sign convention: The matrix can be used to rotate the reference
17840		* frame of a vector. Calling this function with positive phi
17841		* incorporates in the matrix an additional rotation, about the x-axis,
17842		* anticlockwise as seen looking towards the origin from positive x.
17843		*
17844		*<p>Called:<ul>
17845		* <li>{@link #jauIr} initialize r-matrix to identity
17846		* <li>{@link #jauRxr} product of two r-matrices
17847		* <li>{@link #jauCr} copy r-matrix
17848		* </ul>
17849		*@version 2008 May 22
17850		*
17851		* @since Release 20101201
17852		*
17853		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17854		*/
17855		public static void jauRx(double phi, double r[][])
17856		{
17857	382	double s, c, a[][] = new double[3][3], w[][];
17858
17859
17860		/* Matrix representing new rotation. */
17861	382	s = sin(phi);
17862	382	c = cos(phi);
17863	382	jauIr(a);
17864	382	a[1][1] = c;
17865	382	a[2][1] = -s;
17866	382	a[1][2] = s;
17867	382	a[2][2] = c;
17868
17869		/* Rotate. */
17870	382	w = jauRxr(a, r);
17871
17872		/* Return result. */
17873	382	jauCr(w, r);
17874
17875	382	return;
17876
17877		}
17878
17879
17880		/**
17881		* Multiply a p-vector by an r-matrix.
17882		*
17883		*<p>This function is derived from the International Astronomical Union's
17884		* SOFA (Standards Of Fundamental Astronomy) software collection.
17885		*
17886		*<p>Status: vector/matrix support function.
17887		*
17888		*<!-- Given: -->
17889		* @param r double[3][3] r-matrix
17890		* @param p double[3] p-vector
17891		*
17892		*<!-- Returned: -->
17893		* @return rp double[3] <u>returned</u> r * p
17894		*
17895		* Note:
17896		* It is permissible for p and rp to be the same array.
17897		*
17898		*<p>Called:<ul>
17899		* <li>{@link #jauCp} copy p-vector
17900		* </ul>
17901		*@version 2008 October 28
17902		*
17903		* @since Release 20101201
17904		*
17905		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17906		*/
17907		public static double[] jauRxp(double r[][], double p[])
17908		{
17909	120	double w, wrp[] = new double[3] ;
17910		int i, j;
17911
17912
17913		/* Matrix r * vector p. */
17914	480	for (j = 0; j < 3; j++) {
17915	360	w = 0.0;
17916	1440	for (i = 0; i < 3; i++) {
17917	1080	w += r[j][i] * p[i];
17918		}
17919	360	wrp[j] = w;
17920		}
17921
17922
17923	120	return wrp;
17924
17925		}
17926
17927
17928		/**
17929		* Multiply a pv-vector by an r-matrix.
17930		*
17931		*<p>This function is derived from the International Astronomical Union's
17932		* SOFA (Standards Of Fundamental Astronomy) software collection.
17933		*
17934		*<p>Status: vector/matrix support function.
17935		*
17936		*<!-- Given: -->
17937		* @param r double[3][3] r-matrix
17938		* @param pv double[2][3] pv-vector
17939		*
17940		*<!-- Returned: -->
17941		* @return rpv double[2][3] <u>returned</u> r * pv
17942		*
17943		* Note:
17944		* It is permissible for pv and rpv to be the same array.
17945		*
17946		*<p>Called:<ul>
17947		* <li>{@link #jauRxp} product of r-matrix and p-vector
17948		* </ul>
17949		*@version 2008 October 28
17950		*
17951		* @since Release 20101201
17952		*
17953		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17954		*/
17955		public static double[][] jauRxpv(double r[][], double pv[][])
17956		{
17957	16	double rpv[][] = new double[2][0];
17958	16	rpv[0] = jauRxp(r, pv[0]);
17959	16	rpv[1] = jauRxp(r, pv[1]);
17960
17961	16	return rpv;
17962
17963		}
17964
17965
17966		/**
17967		* Multiply two r-matrices.
17968		*
17969		*<p>This function is derived from the International Astronomical Union's
17970		* SOFA (Standards Of Fundamental Astronomy) software collection.
17971		*
17972		*<p>Status: vector/matrix support function.
17973		*
17974		*<!-- Given: -->
17975		* @param a double[3][3] first r-matrix
17976		* @param b double[3][3] second r-matrix
17977		*
17978		*<!-- Returned: -->
17979		* @return atb double[3][3] <u>returned</u> a * b
17980		*
17981		* Note:
17982		* It is permissible to re-use the same array for any of the
17983		* arguments.
17984		*
17985		*<p>Called:<ul>
17986		* <li>{@link #jauCr} copy r-matrix
17987		* </ul>
17988		*@version 2008 November 18
17989		*
17990		* @since Release 20101201
17991		*
17992		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
17993		*/
17994		public static double[][] jauRxr(double a[][], double b[][])
17995		{
17996		int i, j, k;
17997	1080	double w, wm[][] = new double[3][3];
17998
17999
18000	4320	for (i = 0; i < 3; i++) {
18001	12960	for (j = 0; j < 3; j++) {
18002	9720	w = 0.0;
18003	38880	for (k = 0; k < 3; k++) {
18004	29160	w += a[i][k] * b[k][j];
18005		}
18006	9720	wm[i][j] = w;
18007		}
18008		}
18009
18010	1080	return wm;
18011
18012		}
18013
18014
18015		/**
18016		* Rotate an r-matrix about the y-axis.
18017		*
18018		*<p>This function is derived from the International Astronomical Union's
18019		* SOFA (Standards Of Fundamental Astronomy) software collection.
18020		*
18021		*<p>Status: vector/matrix support function.
18022		*
18023		*<!-- Given: -->
18024		* @param theta double angle (radians)
18025		*
18026		* Given and returned:
18027		* @param r double[3][3] <u>given & returned</u> r-matrix
18028		*
18029		* Sign convention: The matrix can be used to rotate the reference
18030		* frame of a vector. Calling This function with positive theta
18031		* incorporates in the matrix an additional rotation, about the y-axis,
18032		* anticlockwise as seen looking towards the origin from positive y.
18033		*
18034		*<p>Called:<ul>
18035		* <li>{@link #jauIr} initialize r-matrix to identity
18036		* <li>{@link #jauRxr} product of two r-matrices
18037		* <li>{@link #jauCr} copy r-matrix
18038		* </ul>
18039		*@version 2008 May 22
18040		*
18041		* @since Release 20101201
18042		*
18043		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18044		*/
18045		public static void jauRy(double theta, double r[][])
18046		{
18047	134	double s, c, a[][] = new double[3][3], w[][];
18048
18049
18050		/* Matrix representing new rotation. */
18051	134	s = sin(theta);
18052	134	c = cos(theta);
18053	134	jauIr(a);
18054	134	a[0][0] = c;
18055	134	a[2][0] = s;
18056	134	a[0][2] = -s;
18057	134	a[2][2] = c;
18058
18059		/* Rotate. */
18060	134	w = jauRxr(a, r);
18061
18062		/* Return result. */
18063	134	jauCr(w, r);
18064
18065	134	return;
18066
18067		}
18068
18069
18070		/**
18071		* Rotate an r-matrix about the z-axis.
18072		*
18073		*<p>This function is derived from the International Astronomical Union's
18074		* SOFA (Standards Of Fundamental Astronomy) software collection.
18075		*
18076		*<p>Status: vector/matrix support function.
18077		*
18078		*<!-- Given: -->
18079		* @param psi double angle (radians)
18080		*
18081		* Given and returned:
18082		* @param r double[3][3] <u>given & retuned</u>r-matrix, rotated
18083		*
18084		* Sign convention: The matrix can be used to rotate the reference
18085		* frame of a vector. Calling This function with positive psi
18086		* incorporates in the matrix an additional rotation, about the z-axis,
18087		* anticlockwise as seen looking towards the origin from positive z.
18088		*
18089		*<p>Called:<ul>
18090		* <li>{@link #jauIr} initialize r-matrix to identity
18091		* <li>{@link #jauRxr} product of two r-matrices
18092		* <li>{@link #jauCr} copy r-matrix
18093		* </ul>
18094		*@version 2008 May 22
18095		*
18096		* @since Release 20101201
18097		*
18098		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18099		*/
18100		public static void jauRz(double psi, double r[][])
18101		{
18102	460	double s, c, a[][] = new double[3][3], w[][];
18103
18104
18105		/* Matrix representing new rotation. */
18106	460	s = sin(psi);
18107	460	c = cos(psi);
18108	460	jauIr(a);
18109	460	a[0][0] = c;
18110	460	a[1][0] = -s;
18111	460	a[0][1] = s;
18112	460	a[1][1] = c;
18113
18114		/* Rotate. */
18115	460	w = jauRxr(a, r);
18116
18117		/* Return result. */
18118	460	jauCr(w, r);
18119
18120	460	return;
18121
18122		}
18123
18124
18125		/**
18126		* The CIO locator s, positioning the Celestial Intermediate Origin on
18127		* the equator of the Celestial Intermediate Pole, given the CIP's X,Y
18128		* coordinates. Compatible with IAU 2000A precession-nutation.
18129		*
18130		*<p>This function is derived from the International Astronomical Union's
18131		* SOFA (Standards Of Fundamental Astronomy) software collection.
18132		*
18133		*<p>Status: canonical model.
18134		*
18135		*<!-- Given: -->
18136		* @param date1 double TT as a 2-part Julian Date (Note 1)
18137		* @param date2 double TT as a 2-part Julian Date (Note 1)
18138		* @param x double CIP coordinates (Note 3)
18139		* @param y double CIP coordinates (Note 3)
18140		*
18141		* <!-- Returned (function value): -->
18142		* @return double the CIO locator s in radians (Note 2)
18143		*
18144		* <p>Notes:
18145		* <ol>
18146		*
18147		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
18148		* convenient way between the two arguments. For example,
18149		* JD(TT)=2450123.7 could be expressed in any of these ways,
18150		* among others:
18151		*<pre>
18152		* date1 date2
18153		*
18154		* 2450123.7 0.0 (JD method)
18155		* 2451545.0 -1421.3 (J2000 method)
18156		* 2400000.5 50123.2 (MJD method)
18157		* 2450123.5 0.2 (date & time method)
18158		*</pre>
18159		* The JD method is the most natural and convenient to use in
18160		* cases where the loss of several decimal digits of resolution
18161		* is acceptable. The J2000 method is best matched to the way
18162		* the argument is handled internally and will deliver the
18163		* optimum resolution. The MJD method and the date & time methods
18164		* are both good compromises between resolution and convenience.
18165		*
18166		* <li> The CIO locator s is the difference between the right ascensions
18167		* of the same point in two systems: the two systems are the GCRS
18168		* and the CIP,CIO, and the point is the ascending node of the
18169		* CIP equator. The quantity s remains below 0.1 arcsecond
18170		* throughout 1900-2100.
18171		*
18172		* <li> The series used to compute s is in fact for s+XY/2, where X and Y
18173		* are the x and y components of the CIP unit vector; this series
18174		* is more compact than a direct series for s would be. This
18175		* function requires X,Y to be supplied by the caller, who is
18176		* responsible for providing values that are consistent with the
18177		* supplied date.
18178		*
18179		* <li> The model is consistent with the IAU 2000A precession-nutation.
18180		*</ol>
18181		*<p>Called:<ul>
18182		* <li>{@link #jauFal03} mean anomaly of the Moon
18183		* <li>{@link #jauFalp03} mean anomaly of the Sun
18184		* <li>{@link #jauFaf03} mean argument of the latitude of the Moon
18185		* <li>{@link #jauFad03} mean elongation of the Moon from the Sun
18186		* <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
18187		* <li>{@link #jauFave03} mean longitude of Venus
18188		* <li>{@link #jauFae03} mean longitude of Earth
18189		* <li>{@link #jauFapa03} general accumulated precession in longitude
18190		* </ul>
18191		*<p>References:
18192		*
18193		* <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
18194		* "Expressions for the Celestial Intermediate Pole and Celestial
18195		* Ephemeris Origin consistent with the IAU 2000A precession-
18196		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
18197		*
18198		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
18199		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
18200		*
18201		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
18202		* IERS Technical Note No. 32, BKG (2004)
18203		*
18204		*@version 2010 January 18
18205		*
18206		* @since Release 20101201
18207		*
18208		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18209		*/
18210		public static double jauS00(double date1, double date2, double x, double y)
18211		{
18212		/* Time since J2000.0, in Julian centuries */
18213		double t;
18214
18215		/* Miscellaneous */
18216		int i, j;
18217		double a, w0, w1, w2, w3, w4, w5;
18218
18219		/* Fundamental arguments */
18220	24	double fa[] = new double[8];
18221
18222		/* Returned value */
18223		double s;
18224
18225		/* --------------------- */
18226		/* The series for s+XY/2 */
18227		/* --------------------- */
18228
18229		/* Polynomial coefficients */
18230	24	final double sp[] = {
18231
18232		/* 1-6 */
18233		94.00e-6,
18234		3808.35e-6,
18235		-119.94e-6,
18236		-72574.09e-6,
18237		27.70e-6,
18238		15.61e-6
18239		};
18240
18241		/* Terms of order t^0 */
18242	24	final TERM s0[] = {
18243
18244		/* 1-10 */
18245		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 ),
18246		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 ),
18247		new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 ),
18248		new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 ),
18249		new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 ),
18250		new TERM(new int[]{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 ),
18251		new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 ),
18252		new TERM(new int[]{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 ),
18253		new TERM(new int[]{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 ),
18254		new TERM(new int[]{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 ),
18255
18256		/* 11-20 */
18257		new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18258		new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18259		new TERM(new int[]{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 ),
18260		new TERM(new int[]{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 ),
18261		new TERM(new int[]{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 ),
18262		new TERM(new int[]{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 ),
18263		new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 ),
18264		new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 ),
18265		new TERM(new int[]{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18266		new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18267
18268		/* 21-30 */
18269		new TERM(new int[]{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 ),
18270		new TERM(new int[]{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 ),
18271		new TERM(new int[]{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 ),
18272		new TERM(new int[]{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 ),
18273		new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 ),
18274		new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18275		new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18276		new TERM(new int[]{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18277		new TERM(new int[]{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18278		new TERM(new int[]{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18279
18280		/* 31-33 */
18281		new TERM(new int[]{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 ),
18282		new TERM(new int[]{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 ),
18283		new TERM(new int[]{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18284		};
18285
18286		/* Terms of order t^1 */
18287	24	final TERM s1[] ={
18288
18289		/* 1-3 */
18290		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 ),
18291		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.71e-6, -0.03e-6 ),
18292		new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 )
18293		};
18294
18295		/* Terms of order t^2 */
18296	24	final TERM s2[] ={
18297
18298		/* 1-10 */
18299		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.53e-6, -0.17e-6 ),
18300		new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 ),
18301		new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 ),
18302		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 ),
18303		new TERM(new int[]{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 ),
18304		new TERM(new int[]{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 ),
18305		new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 ),
18306		new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 ),
18307		new TERM(new int[]{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 ),
18308		new TERM(new int[]{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 ),
18309
18310		/* 11-20 */
18311		new TERM(new int[]{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 ),
18312		new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 ),
18313		new TERM(new int[]{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 ),
18314		new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18315		new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18316		new TERM(new int[]{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18317		new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 ),
18318		new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 ),
18319		new TERM(new int[]{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 ),
18320		new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 ),
18321
18322		/* 21-25 */
18323		new TERM(new int[]{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 ),
18324		new TERM(new int[]{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 ),
18325		new TERM(new int[]{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18326		new TERM(new int[]{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 ),
18327		new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18328		};
18329
18330		/* Terms of order t^3 */
18331	24	final TERM s3[] ={
18332
18333		/* 1-4 */
18334		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.51e-6 ),
18335		new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.39e-6 ),
18336		new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.24e-6 ),
18337		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.22e-6 )
18338		};
18339
18340		/* Terms of order t^4 */
18341	24	final TERM s4[] ={
18342
18343		/* 1-1 */
18344		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 )
18345		};
18346
18347		/* Number of terms in the series */
18348	24	final int NS0 = s0.length;
18349	24	final int NS1 = s1.length;
18350	24	final int NS2 = s2.length;
18351	24	final int NS3 = s3.length;
18352	24	final int NS4 = s4.length;
18353
18354		/--------------------------------------------------------------------/
18355
18356		/* Interval between fundamental epoch J2000.0 and current date (JC). */
18357	24	t = ((date1 - DJ00) + date2) / DJC;
18358
18359		/* Fundamental Arguments (from IERS Conventions 2003) */
18360
18361		/* Mean anomaly of the Moon. */
18362	24	fa[0] = jauFal03(t);
18363
18364		/* Mean anomaly of the Sun. */
18365	24	fa[1] = jauFalp03(t);
18366
18367		/* Mean longitude of the Moon minus that of the ascending node. */
18368	24	fa[2] = jauFaf03(t);
18369
18370		/* Mean elongation of the Moon from the Sun. */
18371	24	fa[3] = jauFad03(t);
18372
18373		/* Mean longitude of the ascending node of the Moon. */
18374	24	fa[4] = jauFaom03(t);
18375
18376		/* Mean longitude of Venus. */
18377	24	fa[5] = jauFave03(t);
18378
18379		/* Mean longitude of Earth. */
18380	24	fa[6] = jauFae03(t);
18381
18382		/* General precession in longitude. */
18383	24	fa[7] = jauFapa03(t);
18384
18385		/* Evaluate s. */
18386	24	w0 = sp[0];
18387	24	w1 = sp[1];
18388	24	w2 = sp[2];
18389	24	w3 = sp[3];
18390	24	w4 = sp[4];
18391	24	w5 = sp[5];
18392
18393	816	for (i = NS0-1; i >= 0; i--) {
18394	792	a = 0.0;
18395	7128	for (j = 0; j < 8; j++) {
18396	6336	a += (double)s0[i].nfa[j] * fa[j];
18397		}
18398	792	w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
18399		}
18400
18401	96	for (i = NS1-1; i >= 0; i--) {
18402	72	a = 0.0;
18403	648	for (j = 0; j < 8; j++) {
18404	576	a += (double)s1[i].nfa[j] * fa[j];
18405		}
18406	72	w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
18407		}
18408
18409	624	for (i = NS2-1; i >= 0; i--) {
18410	600	a = 0.0;
18411	5400	for (j = 0; j < 8; j++) {
18412	4800	a += (double)s2[i].nfa[j] * fa[j];
18413		}
18414	600	w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
18415		}
18416
18417	120	for (i = NS3-1; i >= 0; i--) {
18418	96	a = 0.0;
18419	864	for (j = 0; j < 8; j++) {
18420	768	a += (double)s3[i].nfa[j] * fa[j];
18421		}
18422	96	w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
18423		}
18424
18425	48	for (i = NS4-1; i >= 0; i--) {
18426	24	a = 0.0;
18427	216	for (j = 0; j < 8; j++) {
18428	192	a += (double)s4[i].nfa[j] * fa[j];
18429		}
18430	24	w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
18431		}
18432
18433	24	s = (w0 +
18434		(w1 +
18435		(w2 +
18436		(w3 +
18437		(w4 +
18438		w5 * t) * t) * t) * t) * t) * DAS2R - x*y/2.0;
18439
18440	24	return s;
18441
18442		}
18443
18444
18445		/**
18446		* The CIO locator s, positioning the Celestial Intermediate Origin on
18447		* the equator of the Celestial Intermediate Pole, using the IAU 2000A
18448		* precession-nutation model.
18449		*
18450		*<p>This function is derived from the International Astronomical Union's
18451		* SOFA (Standards Of Fundamental Astronomy) software collection.
18452		*
18453		*<p>Status: support function.
18454		*
18455		*<!-- Given: -->
18456		* @param date1 double TT as a 2-part Julian Date (Note 1)
18457		* @param date2 double TT as a 2-part Julian Date (Note 1)
18458		*
18459		* <!-- Returned (function value): -->
18460		* @return double the CIO locator s in radians (Note 2)
18461		*
18462		* <p>Notes:
18463		* <ol>
18464		*
18465		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
18466		* convenient way between the two arguments. For example,
18467		* JD(TT)=2450123.7 could be expressed in any of these ways,
18468		* among others:
18469		*<pre>
18470		* date1 date2
18471		*
18472		* 2450123.7 0.0 (JD method)
18473		* 2451545.0 -1421.3 (J2000 method)
18474		* 2400000.5 50123.2 (MJD method)
18475		* 2450123.5 0.2 (date & time method)
18476		*</pre>
18477		* The JD method is the most natural and convenient to use in
18478		* cases where the loss of several decimal digits of resolution
18479		* is acceptable. The J2000 method is best matched to the way
18480		* the argument is handled internally and will deliver the
18481		* optimum resolution. The MJD method and the date & time methods
18482		* are both good compromises between resolution and convenience.
18483		*
18484		* <li> The CIO locator s is the difference between the right ascensions
18485		* of the same point in two systems. The two systems are the GCRS
18486		* and the CIP,CIO, and the point is the ascending node of the
18487		* CIP equator. The CIO locator s remains a small fraction of
18488		* 1 arcsecond throughout 1900-2100.
18489		*
18490		* <li> The series used to compute s is in fact for s+XY/2, where X and Y
18491		* are the x and y components of the CIP unit vector; this series
18492		* is more compact than a direct series for s would be. The present
18493		* function uses the full IAU 2000A nutation model when predicting
18494		* the CIP position. Faster results, with no significant loss of
18495		* accuracy, can be obtained via the function jauS00b, which uses
18496		* instead the IAU 2000B truncated model.
18497		*</ol>
18498		*<p>Called:<ul>
18499		* <li>{@link #jauPnm00a} classical NPB matrix, IAU 2000A
18500		* <li>{@link #jauBpn2xy} extract CIP X,Y from the BPN matrix
18501		* <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
18502		* </ul>
18503		*<p>References:
18504		*
18505		* <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
18506		* "Expressions for the Celestial Intermediate Pole and Celestial
18507		* Ephemeris Origin consistent with the IAU 2000A precession-
18508		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
18509		*
18510		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
18511		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
18512		*
18513		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
18514		* IERS Technical Note No. 32, BKG (2004)
18515		*
18516		*@version 2010 January 18
18517		*
18518		* @since Release 20101201
18519		*
18520		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18521		*/
18522		public static double jauS00a(double date1, double date2)
18523		{
18524		double s;
18525
18526
18527		/* Bias-precession-nutation-matrix, IAU 2000A. */
18528	2	double rbpn[][] = jauPnm00a(date1, date2);
18529
18530		/* Extract the CIP coordinates. */
18531	2	CelestialIntermediatePole cip = jauBpn2xy(rbpn);
18532
18533		/* Compute the CIO locator s, given the CIP coordinates. */
18534	2	s = jauS00(date1, date2, cip.x, cip.y);
18535
18536	2	return s;
18537
18538		}
18539
18540
18541		/**
18542		* The CIO locator s, positioning the Celestial Intermediate Origin on
18543		* the equator of the Celestial Intermediate Pole, using the IAU 2000B
18544		* precession-nutation model.
18545		*
18546		*<p>This function is derived from the International Astronomical Union's
18547		* SOFA (Standards Of Fundamental Astronomy) software collection.
18548		*
18549		*<p>Status: support function.
18550		*
18551		*<!-- Given: -->
18552		* @param date1 double TT as a 2-part Julian Date (Note 1)
18553		* @param date2 double TT as a 2-part Julian Date (Note 1)
18554		*
18555		* <!-- Returned (function value): -->
18556		* @return double the CIO locator s in radians (Note 2)
18557		*
18558		* <p>Notes:
18559		* <ol>
18560		*
18561		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
18562		* convenient way between the two arguments. For example,
18563		* JD(TT)=2450123.7 could be expressed in any of these ways,
18564		* among others:
18565		*<pre>
18566		* date1 date2
18567		*
18568		* 2450123.7 0.0 (JD method)
18569		* 2451545.0 -1421.3 (J2000 method)
18570		* 2400000.5 50123.2 (MJD method)
18571		* 2450123.5 0.2 (date & time method)
18572		*</pre>
18573		* The JD method is the most natural and convenient to use in
18574		* cases where the loss of several decimal digits of resolution
18575		* is acceptable. The J2000 method is best matched to the way
18576		* the argument is handled internally and will deliver the
18577		* optimum resolution. The MJD method and the date & time methods
18578		* are both good compromises between resolution and convenience.
18579		*
18580		* <li> The CIO locator s is the difference between the right ascensions
18581		* of the same point in two systems. The two systems are the GCRS
18582		* and the CIP,CIO, and the point is the ascending node of the
18583		* CIP equator. The CIO locator s remains a small fraction of
18584		* 1 arcsecond throughout 1900-2100.
18585		*
18586		* <li> The series used to compute s is in fact for s+XY/2, where X and Y
18587		* are the x and y components of the CIP unit vector; this series
18588		* is more compact than a direct series for s would be. The present
18589		* function uses the IAU 2000B truncated nutation model when
18590		* predicting the CIP position. The function jauS00a uses instead
18591		* the full IAU 2000A model, but with no significant increase in
18592		* accuracy and at some cost in speed.
18593		*</ol>
18594		*<p>Called:<ul>
18595		* <li>{@link #jauPnm00b} classical NPB matrix, IAU 2000B
18596		* <li>{@link #jauBpn2xy} extract CIP X,Y from the BPN matrix
18597		* <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
18598		* </ul>
18599		*<p>References:
18600		*
18601		* <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
18602		* "Expressions for the Celestial Intermediate Pole and Celestial
18603		* Ephemeris Origin consistent with the IAU 2000A precession-
18604		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
18605		*
18606		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
18607		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
18608		*
18609		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
18610		* IERS Technical Note No. 32, BKG (2004)
18611		*
18612		*@version 2010 January 18
18613		*
18614		* @since Release 20101201
18615		*
18616		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18617		*/
18618		public static double jauS00b(double date1, double date2)
18619		{
18620	2	double rbpn[][] = new double[3][3], s;
18621
18622
18623		/* Bias-precession-nutation-matrix, IAU 2000B. */
18624	2	rbpn = jauPnm00b(date1, date2);
18625
18626		/* Extract the CIP coordinates. */
18627	2	CelestialIntermediatePole cip = jauBpn2xy(rbpn);
18628
18629		/* Compute the CIO locator s, given the CIP coordinates. */
18630	2	s = jauS00(date1, date2, cip.x, cip.y);
18631
18632	2	return s;
18633
18634		}
18635
18636
18637		/**
18638		* The CIO locator s, positioning the Celestial Intermediate Origin on
18639		* the equator of the Celestial Intermediate Pole, given the CIP's X,Y
18640		* coordinates. Compatible with IAU 2006/2000A precession-nutation.
18641		*
18642		*<p>This function is derived from the International Astronomical Union's
18643		* SOFA (Standards Of Fundamental Astronomy) software collection.
18644		*
18645		*<p>Status: canonical model.
18646		*
18647		*<!-- Given: -->
18648		* @param date1 double TT as a 2-part Julian Date (Note 1)
18649		* @param date2 double TT as a 2-part Julian Date (Note 1)
18650		* @param x double CIP coordinates (Note 3)
18651		* @param y double CIP coordinates (Note 3)
18652		*
18653		* <!-- Returned (function value): -->
18654		* @return double the CIO locator s in radians (Note 2)
18655		*
18656		* <p>Notes:
18657		* <ol>
18658		*
18659		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
18660		* convenient way between the two arguments. For example,
18661		* JD(TT)=2450123.7 could be expressed in any of these ways,
18662		* among others:
18663		*<pre>
18664		* date1 date2
18665		*
18666		* 2450123.7 0.0 (JD method)
18667		* 2451545.0 -1421.3 (J2000 method)
18668		* 2400000.5 50123.2 (MJD method)
18669		* 2450123.5 0.2 (date & time method)
18670		*</pre>
18671		* The JD method is the most natural and convenient to use in
18672		* cases where the loss of several decimal digits of resolution
18673		* is acceptable. The J2000 method is best matched to the way
18674		* the argument is handled internally and will deliver the
18675		* optimum resolution. The MJD method and the date & time methods
18676		* are both good compromises between resolution and convenience.
18677		*
18678		* <li> The CIO locator s is the difference between the right ascensions
18679		* of the same point in two systems: the two systems are the GCRS
18680		* and the CIP,CIO, and the point is the ascending node of the
18681		* CIP equator. The quantity s remains below 0.1 arcsecond
18682		* throughout 1900-2100.
18683		*
18684		* <li> The series used to compute s is in fact for s+XY/2, where X and Y
18685		* are the x and y components of the CIP unit vector; this series
18686		* is more compact than a direct series for s would be. This
18687		* function requires X,Y to be supplied by the caller, who is
18688		* responsible for providing values that are consistent with the
18689		* supplied date.
18690		*
18691		* <li> The model is consistent with the "P03" precession (Capitaine et
18692		* al. 2003), adopted by IAU 2006 Resolution 1, 2006, and the
18693		* IAU 2000A nutation (with P03 adjustments).
18694		*</ol>
18695		*<p>Called:<ul>
18696		* <li>{@link #jauFal03} mean anomaly of the Moon
18697		* <li>{@link #jauFalp03} mean anomaly of the Sun
18698		* <li>{@link #jauFaf03} mean argument of the latitude of the Moon
18699		* <li>{@link #jauFad03} mean elongation of the Moon from the Sun
18700		* <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
18701		* <li>{@link #jauFave03} mean longitude of Venus
18702		* <li>{@link #jauFae03} mean longitude of Earth
18703		* <li>{@link #jauFapa03} general accumulated precession in longitude
18704		* </ul>
18705		*<p>References:
18706		*
18707		* <p>Capitaine, N., Wallace, P.T. & Chapront, J., 2003, Astron.
18708		* Astrophys. 432, 355
18709		*
18710		* <p>McCarthy, D.D., Petit, G. (eds.) 2004, IERS Conventions (2003),
18711		* IERS Technical Note No. 32, BKG
18712		*
18713		*@version 2009 December 17
18714		*
18715		* @since Release 20101201
18716		*
18717		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
18718		*/
18719		public static double jauS06(double date1, double date2, double x, double y)
18720		{
18721		/* Time since J2000.0, in Julian centuries */
18722		double t;
18723
18724		/* Miscellaneous */
18725		int i, j;
18726		double a, w0, w1, w2, w3, w4, w5;
18727
18728		/* Fundamental arguments */
18729	44	double fa[] = new double[8];
18730
18731		/* Returned value */
18732		double s;
18733
18734		/* --------------------- */
18735		/* The series for s+XY/2 */
18736		/* --------------------- */
18737
18738		/* Polynomial coefficients */
18739	44	final double sp[] = {
18740
18741		/* 1-6 */
18742		94.00e-6,
18743		3808.65e-6,
18744		-122.68e-6,
18745		-72574.11e-6,
18746		27.98e-6,
18747		15.62e-6
18748		};
18749
18750		/* Terms of order t^0 */
18751	44	final TERM s0[] = {
18752
18753		/* 1-10 */
18754		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -2640.73e-6, 0.39e-6 ),
18755		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -63.53e-6, 0.02e-6 ),
18756		new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, -11.75e-6, -0.01e-6 ),
18757		new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -11.21e-6, -0.01e-6 ),
18758		new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 4.57e-6, 0.00e-6 ),
18759		new TERM(new int[]{ 0, 0, 2, 0, 3, 0, 0, 0}, -2.02e-6, 0.00e-6 ),
18760		new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, -1.98e-6, 0.00e-6 ),
18761		new TERM(new int[]{ 0, 0, 0, 0, 3, 0, 0, 0}, 1.72e-6, 0.00e-6 ),
18762		new TERM(new int[]{ 0, 1, 0, 0, 1, 0, 0, 0}, 1.41e-6, 0.01e-6 ),
18763		new TERM(new int[]{ 0, 1, 0, 0, -1, 0, 0, 0}, 1.26e-6, 0.01e-6 ),
18764
18765		/* 11-20 */
18766		new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18767		new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, 0.63e-6, 0.00e-6 ),
18768		new TERM(new int[]{ 0, 1, 2, -2, 3, 0, 0, 0}, -0.46e-6, 0.00e-6 ),
18769		new TERM(new int[]{ 0, 1, 2, -2, 1, 0, 0, 0}, -0.45e-6, 0.00e-6 ),
18770		new TERM(new int[]{ 0, 0, 4, -4, 4, 0, 0, 0}, -0.36e-6, 0.00e-6 ),
18771		new TERM(new int[]{ 0, 0, 1, -1, 1, -8, 12, 0}, 0.24e-6, 0.12e-6 ),
18772		new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.32e-6, 0.00e-6 ),
18773		new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.28e-6, 0.00e-6 ),
18774		new TERM(new int[]{ 1, 0, 2, 0, 3, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18775		new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18776
18777		/* 21-30 */
18778		new TERM(new int[]{ 0, 0, 2, -2, 0, 0, 0, 0}, 0.21e-6, 0.00e-6 ),
18779		new TERM(new int[]{ 0, 1, -2, 2, -3, 0, 0, 0}, -0.19e-6, 0.00e-6 ),
18780		new TERM(new int[]{ 0, 1, -2, 2, -1, 0, 0, 0}, -0.18e-6, 0.00e-6 ),
18781		new TERM(new int[]{ 0, 0, 0, 0, 0, 8,-13, -1}, 0.10e-6, -0.05e-6 ),
18782		new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.15e-6, 0.00e-6 ),
18783		new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18784		new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 0.14e-6, 0.00e-6 ),
18785		new TERM(new int[]{ 1, 0, 0, -2, 1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18786		new TERM(new int[]{ 1, 0, 0, -2, -1, 0, 0, 0}, -0.14e-6, 0.00e-6 ),
18787		new TERM(new int[]{ 0, 0, 4, -2, 4, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18788
18789		/* 31-33 */
18790		new TERM(new int[]{ 0, 0, 2, -2, 4, 0, 0, 0}, 0.11e-6, 0.00e-6 ),
18791		new TERM(new int[]{ 1, 0, -2, 0, -3, 0, 0, 0}, -0.11e-6, 0.00e-6 ),
18792		new TERM(new int[]{ 1, 0, -2, 0, -1, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18793		};
18794
18795		/* Terms of order t^1 */
18796	44	final TERM s1[] = {
18797
18798		/* 1 - 3 */
18799		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -0.07e-6, 3.57e-6 ),
18800		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 1.73e-6, -0.03e-6 ),
18801		new TERM(new int[]{ 0, 0, 2, -2, 3, 0, 0, 0}, 0.00e-6, 0.48e-6 )
18802		};
18803
18804		/* Terms of order t^2 */
18805	44	final TERM s2[] = {
18806
18807		/* 1-10 */
18808		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 743.52e-6, -0.17e-6 ),
18809		new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, 56.91e-6, 0.06e-6 ),
18810		new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, 9.84e-6, -0.01e-6 ),
18811		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, -8.85e-6, 0.01e-6 ),
18812		new TERM(new int[]{ 0, 1, 0, 0, 0, 0, 0, 0}, -6.38e-6, -0.05e-6 ),
18813		new TERM(new int[]{ 1, 0, 0, 0, 0, 0, 0, 0}, -3.07e-6, 0.00e-6 ),
18814		new TERM(new int[]{ 0, 1, 2, -2, 2, 0, 0, 0}, 2.23e-6, 0.00e-6 ),
18815		new TERM(new int[]{ 0, 0, 2, 0, 1, 0, 0, 0}, 1.67e-6, 0.00e-6 ),
18816		new TERM(new int[]{ 1, 0, 2, 0, 2, 0, 0, 0}, 1.30e-6, 0.00e-6 ),
18817		new TERM(new int[]{ 0, 1, -2, 2, -2, 0, 0, 0}, 0.93e-6, 0.00e-6 ),
18818
18819		/* 11-20 */
18820		new TERM(new int[]{ 1, 0, 0, -2, 0, 0, 0, 0}, 0.68e-6, 0.00e-6 ),
18821		new TERM(new int[]{ 0, 0, 2, -2, 1, 0, 0, 0}, -0.55e-6, 0.00e-6 ),
18822		new TERM(new int[]{ 1, 0, -2, 0, -2, 0, 0, 0}, 0.53e-6, 0.00e-6 ),
18823		new TERM(new int[]{ 0, 0, 0, 2, 0, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18824		new TERM(new int[]{ 1, 0, 0, 0, 1, 0, 0, 0}, -0.27e-6, 0.00e-6 ),
18825		new TERM(new int[]{ 1, 0, -2, -2, -2, 0, 0, 0}, -0.26e-6, 0.00e-6 ),
18826		new TERM(new int[]{ 1, 0, 0, 0, -1, 0, 0, 0}, -0.25e-6, 0.00e-6 ),
18827		new TERM(new int[]{ 1, 0, 2, 0, 1, 0, 0, 0}, 0.22e-6, 0.00e-6 ),
18828		new TERM(new int[]{ 2, 0, 0, -2, 0, 0, 0, 0}, -0.21e-6, 0.00e-6 ),
18829		new TERM(new int[]{ 2, 0, -2, 0, -1, 0, 0, 0}, 0.20e-6, 0.00e-6 ),
18830
18831		/* 21-25 */
18832		new TERM(new int[]{ 0, 0, 2, 2, 2, 0, 0, 0}, 0.17e-6, 0.00e-6 ),
18833		new TERM(new int[]{ 2, 0, 2, 0, 2, 0, 0, 0}, 0.13e-6, 0.00e-6 ),
18834		new TERM(new int[]{ 2, 0, 0, 0, 0, 0, 0, 0}, -0.13e-6, 0.00e-6 ),
18835		new TERM(new int[]{ 1, 0, 2, -2, 2, 0, 0, 0}, -0.12e-6, 0.00e-6 ),
18836		new TERM(new int[]{ 0, 0, 2, 0, 0, 0, 0, 0}, -0.11e-6, 0.00e-6 )
18837		};
18838
18839		/* Terms of order t^3 */
18840	44	final TERM s3[] = {
18841
18842		/* 1-4 */
18843		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, 0.30e-6, -23.42e-6 ),
18844		new TERM(new int[]{ 0, 0, 2, -2, 2, 0, 0, 0}, -0.03e-6, -1.46e-6 ),
18845		new TERM(new int[]{ 0, 0, 2, 0, 2, 0, 0, 0}, -0.01e-6, -0.25e-6 ),
18846		new TERM(new int[]{ 0, 0, 0, 0, 2, 0, 0, 0}, 0.00e-6, 0.23e-6 )
18847		};
18848
18849		/* Terms of order t^4 */
18850	44	final TERM s4[] = {
18851
18852		/* 1-1 */
18853		new TERM(new int[]{ 0, 0, 0, 0, 1, 0, 0, 0}, -0.26e-6, -0.01e-6 )
18854		};
18855
18856		/* Number of terms in the series */
18857	44	final int NS0 = s0.length;
18858	44	final int NS1 = s1.length;
18859	44	final int NS2 = s2.length;
18860	44	final int NS3 = s3.length;
18861	44	final int NS4 = s4.length;
18862
18863		/--------------------------------------------------------------------/
18864
18865		/* Interval between fundamental epoch J2000.0 and current date (JC). */
18866	44	t = ((date1 - DJ00) + date2) / DJC;
18867
18868		/* Fundamental Arguments (from IERS Conventions 2003) */
18869
18870		/* Mean anomaly of the Moon. */
18871	44	fa[0] = jauFal03(t);
18872
18873		/* Mean anomaly of the Sun. */
18874	44	fa[1] = jauFalp03(t);
18875
18876		/* Mean longitude of the Moon minus that of the ascending node. */
18877	44	fa[2] = jauFaf03(t);
18878
18879		/* Mean elongation of the Moon from the Sun. */
18880	44	fa[3] = jauFad03(t);
18881
18882		/* Mean longitude of the ascending node of the Moon. */
18883	44	fa[4] = jauFaom03(t);
18884
18885		/* Mean longitude of Venus. */
18886	44	fa[5] = jauFave03(t);
18887
18888		/* Mean longitude of Earth. */
18889	44	fa[6] = jauFae03(t);
18890
18891		/* General precession in longitude. */
18892	44	fa[7] = jauFapa03(t);
18893
18894		/* Evaluate s. */
18895	44	w0 = sp[0];
18896	44	w1 = sp[1];
18897	44	w2 = sp[2];
18898	44	w3 = sp[3];
18899	44	w4 = sp[4];
18900	44	w5 = sp[5];
18901
18902	1496	for (i = NS0-1; i >= 0; i--) {
18903	1452	a = 0.0;
18904	13068	for (j = 0; j < 8; j++) {
18905	11616	a += (double)s0[i].nfa[j] * fa[j];
18906		}
18907	1452	w0 += s0[i].s * sin(a) + s0[i].c * cos(a);
18908		}
18909
18910	176	for (i = NS1-1; i >= 0; i--) {
18911	132	a = 0.0;
18912	1188	for (j = 0; j < 8; j++) {
18913	1056	a += (double)s1[i].nfa[j] * fa[j];
18914		}
18915	132	w1 += s1[i].s * sin(a) + s1[i].c * cos(a);
18916		}
18917
18918	1144	for (i = NS2-1; i >= 0; i--) {
18919	1100	a = 0.0;
18920	9900	for (j = 0; j < 8; j++) {
18921	8800	a += (double)s2[i].nfa[j] * fa[j];
18922		}
18923	1100	w2 += s2[i].s * sin(a) + s2[i].c * cos(a);
18924		}
18925
18926	220	for (i = NS3-1; i >= 0; i--) {
18927	176	a = 0.0;
18928	1584	for (j = 0; j < 8; j++) {
18929	1408	a += (double)s3[i].nfa[j] * fa[j];
18930		}
18931	176	w3 += s3[i].s * sin(a) + s3[i].c * cos(a);
18932		}
18933
18934	88	for (i = NS4-1; i >= 0; i--) {
18935	44	a = 0.0;
18936	396	for (j = 0; j < 8; j++) {
18937	352	a += (double)s4[i].nfa[j] * fa[j];
18938		}
18939	44	w4 += s4[i].s * sin(a) + s4[i].c * cos(a);
18940		}
18941
18942	44	s = (w0 +
18943		(w1 +
18944		(w2 +
18945		(w3 +
18946		(w4 +
18947		w5 * t) * t) * t) * t) * t) * DAS2R - x*y/2.0;
18948
18949	44	return s;
18950
18951		}
18952
18953
18954		/**
18955		* The CIO locator s, positioning the Celestial Intermediate Origin on
18956		* the equator of the Celestial Intermediate Pole, using the IAU 2006
18957		* precession and IAU 2000A nutation models.
18958		*
18959		*<p>This function is derived from the International Astronomical Union's
18960		* SOFA (Standards Of Fundamental Astronomy) software collection.
18961		*
18962		*<p>Status: support function.
18963		*
18964		*<!-- Given: -->
18965		* @param date1 double TT as a 2-part Julian Date (Note 1)
18966		* @param date2 double TT as a 2-part Julian Date (Note 1)
18967		*
18968		* <!-- Returned (function value): -->
18969		* @return double the CIO locator s in radians (Note 2)
18970		*
18971		* <p>Notes:
18972		* <ol>
18973		*
18974		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
18975		* convenient way between the two arguments. For example,
18976		* JD(TT)=2450123.7 could be expressed in any of these ways,
18977		* among others:
18978		*<pre>
18979		* date1 date2
18980		*
18981		* 2450123.7 0.0 (JD method)
18982		* 2451545.0 -1421.3 (J2000 method)
18983		* 2400000.5 50123.2 (MJD method)
18984		* 2450123.5 0.2 (date & time method)
18985		*</pre>
18986		* The JD method is the most natural and convenient to use in
18987		* cases where the loss of several decimal digits of resolution
18988		* is acceptable. The J2000 method is best matched to the way
18989		* the argument is handled internally and will deliver the
18990		* optimum resolution. The MJD method and the date & time methods
18991		* are both good compromises between resolution and convenience.
18992		*
18993		* <li> The CIO locator s is the difference between the right ascensions
18994		* of the same point in two systems. The two systems are the GCRS
18995		* and the CIP,CIO, and the point is the ascending node of the
18996		* CIP equator. The CIO locator s remains a small fraction of
18997		* 1 arcsecond throughout 1900-2100.
18998		*
18999		* <li> The series used to compute s is in fact for s+XY/2, where X and Y
19000		* are the x and y components of the CIP unit vector; this series is
19001		* more compact than a direct series for s would be. The present
19002		* function uses the full IAU 2000A nutation model when predicting
19003		* the CIP position.
19004		*</ol>
19005		*<p>Called:<ul>
19006		* <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
19007		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
19008		* <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
19009		* </ul>
19010		*<p>References:
19011		*
19012		* <p>Capitaine, N., Chapront, J., Lambert, S. and Wallace, P.,
19013		* "Expressions for the Celestial Intermediate Pole and Celestial
19014		* Ephemeris Origin consistent with the IAU 2000A precession-
19015		* nutation model", Astron.Astrophys. 400, 1145-1154 (2003)
19016		*
19017		* n.b. The celestial ephemeris origin (CEO) was renamed "celestial
19018		* intermediate origin" (CIO) by IAU 2006 Resolution 2.
19019		*
19020		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
19021		*
19022		* <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
19023		* IERS Technical Note No. 32, BKG
19024		*
19025		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
19026		*
19027		*@version 2010 January 18
19028		*
19029		* @since Release 20101201
19030		*
19031		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19032		*/
19033		public static double jauS06a(double date1, double date2)
19034		{
19035	2	double rnpb[][] = new double[3][3], s;
19036
19037
19038		/* Bias-precession-nutation-matrix, IAU 20006/2000A. */
19039	2	rnpb = jauPnm06a(date1, date2);
19040
19041		/* Extract the CIP coordinates. */
19042	2	CelestialIntermediatePole cip = jauBpn2xy(rnpb);
19043
19044		/* Compute the CIO locator s, given the CIP coordinates. */
19045	2	s = jauS06(date1, date2, cip.x, cip.y);
19046
19047	2	return s;
19048
19049		}
19050
19051
19052		/**
19053		* Convert spherical coordinates to Cartesian.
19054		*
19055		*<p>This function is derived from the International Astronomical Union's
19056		* SOFA (Standards Of Fundamental Astronomy) software collection.
19057		*
19058		*<p>Status: vector/matrix support function.
19059		*
19060		*<!-- Given: -->
19061		* @param theta double longitude angle (radians)
19062		* @param phi double latitude angle (radians)
19063		*
19064		*<!-- Returned: -->
19065		* @return c double[3] <u>returned</u> direction cosines
19066		*
19067		*@version 2008 October 28
19068		*
19069		* @since Release 20101201
19070		*
19071		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19072		*/
19073		public static double[] jauS2c(double theta, double phi )
19074		{
19075	60	double cp, c[] = new double[3];
19076
19077
19078	60	cp = cos(phi);
19079	60	c[0] = cos(theta) * cp;
19080	60	c[1] = sin(theta) * cp;
19081	60	c[2] = sin(phi);
19082
19083	60	return c;
19084
19085		}
19086
19087
19088		/**
19089		* Convert spherical polar coordinates to p-vector.
19090		*
19091		*<p>This function is derived from the International Astronomical Union's
19092		* SOFA (Standards Of Fundamental Astronomy) software collection.
19093		*
19094		*<p>Status: vector/matrix support function.
19095		*
19096		*<!-- Given: -->
19097		* @param theta double longitude angle (radians)
19098		* @param phi double latitude angle (radians)
19099		* @param r double radial distance
19100		*
19101		*<!-- Returned: -->
19102		* @return p double[3] <u>returned</u> Cartesian coordinates
19103		*
19104		*<p>Called:<ul>
19105		* <li>{@link #jauS2c} spherical coordinates to unit vector
19106		* <li>{@link #jauSxp} multiply p-vector by scalar
19107		* </ul>
19108		*@version 2008 May 11
19109		*
19110		* @since Release 20101201
19111		*
19112		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19113		*/
19114		public static double[] jauS2p(double theta, double phi, double r )
19115		{
19116		double p[];
19117	2	double u[] = new double[3];
19118
19119
19120	2	u = jauS2c(theta,phi);
19121	2	p = jauSxp(r,u);
19122
19123	2	return p;
19124
19125		}
19126
19127
19128		/**
19129		* Convert position/velocity from spherical to Cartesian coordinates.
19130		*
19131		*<p>This function is derived from the International Astronomical Union's
19132		* SOFA (Standards Of Fundamental Astronomy) software collection.
19133		*
19134		*<p>Status: vector/matrix support function.
19135		*
19136		*<!-- Given: -->
19137		* @param theta double longitude angle (radians)
19138		* @param phi double latitude angle (radians)
19139		* @param r double radial distance
19140		* @param td double rate of change of theta
19141		* @param pd double rate of change of phi
19142		* @param rd double rate of change of r
19143		*
19144		*<!-- Returned: -->
19145		* @return pv double[2][3] <u>returned</u> pv-vector
19146		*
19147		*@version 2008 May 25
19148		*
19149		* @since Release 20101201
19150		*
19151		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19152		*/
19153		public static double[][] jauS2pv(double theta, double phi, double r,
19154		double td, double pd, double rd)
19155		{
19156	12	double pv[][] = new double[2][3];
19157		double st, ct, sp, cp, rcp, x, y, rpd, w;
19158
19159
19160	12	st = sin(theta);
19161	12	ct = cos(theta);
19162	12	sp = sin(phi);
19163	12	cp = cos(phi);
19164	12	rcp = r * cp;
19165	12	x = rcp * ct;
19166	12	y = rcp * st;
19167	12	rpd = r * pd;
19168	12	w = rpdsp - cprd;
19169
19170	12	pv[0][0] = x;
19171	12	pv[0][1] = y;
19172	12	pv[0][2] = r * sp;
19173	12	pv[1][0] = -ytd - wct;
19174	12	pv[1][1] = xtd - wst;
19175	12	pv[1][2] = rpdcp + sprd;
19176
19177	12	return pv;
19178
19179		}
19180
19181
19182		/**
19183		* Multiply a pv-vector by two scalars.
19184		*
19185		*<p>This function is derived from the International Astronomical Union's
19186		* SOFA (Standards Of Fundamental Astronomy) software collection.
19187		*
19188		*<p>Status: vector/matrix support function.
19189		*
19190		*<!-- Given: -->
19191		* @param s1 double scalar to multiply position component by
19192		* @param s2 double scalar to multiply velocity component by
19193		* @param pv double[2][3] pv-vector
19194		*
19195		*<!-- Returned: -->
19196		* @return spv double[2][3] <u>returned</u> pv-vector: p scaled by s1, v scaled by s2
19197		*
19198		* Note:
19199		* It is permissible for pv and spv to be the same array.
19200		*
19201		*<p>Called:<ul>
19202		* <li>{@link #jauSxp} multiply p-vector by scalar
19203		* </ul>
19204		*@version 2008 October 28
19205		*
19206		* @since Release 20101201
19207		*
19208		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19209		*/
19210		public static double[][] jauS2xpv(double s1, double s2, double pv[][])
19211		{
19212	4	double spv[][] = new double[2][3];
19213	4	spv[0] = jauSxp(s1, pv[0]);
19214	4	spv[1] =jauSxp(s2, pv[1]);
19215
19216	4	return spv;
19217
19218		}
19219
19220
19221		/**
19222		* Angular separation between two p-vectors.
19223		*
19224		*<p>This function is derived from the International Astronomical Union's
19225		* SOFA (Standards Of Fundamental Astronomy) software collection.
19226		*
19227		*<p>Status: vector/matrix support function.
19228		*
19229		*<!-- Given: -->
19230		* @param a double[3] first p-vector (not necessarily unit length)
19231		* @param b double[3] second p-vector (not necessarily unit length)
19232		*
19233		* <!-- Returned (function value): -->
19234		* @return double angular separation (radians, always positive)
19235		*
19236		* <p>Notes:
19237		* <ol>
19238		*
19239		* <li> If either vector is null, a zero result is returned.
19240		*
19241		* <li> The angular separation is most simply formulated in terms of
19242		* scalar product. However, this gives poor accuracy for angles
19243		* near zero and pi. The present algorithm uses both cross product
19244		* and dot product, to deliver full accuracy whatever the size of
19245		* the angle.
19246		*</ol>
19247		*<p>Called:<ul>
19248		* <li>{@link #jauPxp} vector product of two p-vectors
19249		* <li>{@link #jauPm} modulus of p-vector
19250		* <li>{@link #jauPdp} scalar product of two p-vectors
19251		* </ul>
19252		*@version 2008 May 22
19253		*
19254		* @since Release 20101201
19255		*
19256		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19257		*/
19258		public static double jauSepp(double a[] , double b[] )
19259		{
19260	6	double axb[] = new double[3], ss, cs, s;
19261
19262
19263		/* Sine of angle between the vectors, multiplied by the two moduli. */
19264	6	axb = jauPxp(a,b);
19265	6	ss = jauPm(axb);
19266
19267		/* Cosine of the angle, multiplied by the two moduli. */
19268	6	cs = jauPdp(a, b);
19269
19270		/* The angle. */
19271	6	s = ((ss != 0.0) \|\| (cs != 0.0)) ? atan2(ss, cs) : 0.0;
19272
19273	6	return s;
19274
19275		}
19276
19277
19278		/**
19279		* Angular separation between two sets of spherical coordinates.
19280		*
19281		*<p>This function is derived from the International Astronomical Union's
19282		* SOFA (Standards Of Fundamental Astronomy) software collection.
19283		*
19284		*<p>Status: vector/matrix support function.
19285		*
19286		*<!-- Given: -->
19287		* @param al double first longitude (radians)
19288		* @param ap double first latitude (radians)
19289		* @param bl double second longitude (radians)
19290		* @param bp double second latitude (radians)
19291		*
19292		* <!-- Returned (function value): -->
19293		* @return double angular separation (radians)
19294		*
19295		*<p>Called:<ul>
19296		* <li>{@link #jauS2c} spherical coordinates to unit vector
19297		* <li>{@link #jauSepp} angular separation between two p-vectors
19298		* </ul>
19299		*@version 2008 May 16
19300		*
19301		* @since Release 20101201
19302		*
19303		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19304		*/
19305		public static double jauSeps(double al, double ap, double bl, double bp)
19306		{
19307	4	double ac[] = new double[3], bc[] = new double[3], s;
19308
19309
19310		/* Spherical to Cartesian. */
19311	4	ac = jauS2c(al,ap);
19312	4	bc = jauS2c(bl,bp);
19313
19314		/* Angle between the vectors. */
19315	4	s = jauSepp(ac, bc);
19316
19317	4	return s;
19318
19319		}
19320
19321
19322		/**
19323		* The TIO locator s', positioning the Terrestrial Intermediate Origin
19324		* on the equator of the Celestial Intermediate Pole.
19325		*
19326		*<p>This function is derived from the International Astronomical Union's
19327		* SOFA (Standards Of Fundamental Astronomy) software collection.
19328		*
19329		*<p>Status: canonical model.
19330		*
19331		*<!-- Given: -->
19332		* @param date1 double TT as a 2-part Julian Date (Note 1)
19333		* @param date2 double TT as a 2-part Julian Date (Note 1)
19334		*
19335		* <!-- Returned (function value): -->
19336		* @return double the TIO locator s' in radians (Note 2)
19337		*
19338		* <p>Notes:
19339		* <ol>
19340		*
19341		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
19342		* convenient way between the two arguments. For example,
19343		* JD(TT)=2450123.7 could be expressed in any of these ways,
19344		* among others:
19345		*<pre>
19346		* date1 date2
19347		*
19348		* 2450123.7 0.0 (JD method)
19349		* 2451545.0 -1421.3 (J2000 method)
19350		* 2400000.5 50123.2 (MJD method)
19351		* 2450123.5 0.2 (date & time method)
19352		*</pre>
19353		* The JD method is the most natural and convenient to use in
19354		* cases where the loss of several decimal digits of resolution
19355		* is acceptable. The J2000 method is best matched to the way
19356		* the argument is handled internally and will deliver the
19357		* optimum resolution. The MJD method and the date & time methods
19358		* are both good compromises between resolution and convenience.
19359		*
19360		* <li> The TIO locator s' is obtained from polar motion observations by
19361		* numerical integration, and so is in essence unpredictable.
19362		* However, it is dominated by a secular drift of about
19363		* 47 microarcseconds per century, which is the approximation
19364		* evaluated by the present function.
19365		*</ol>
19366		*<p>Reference:
19367		*
19368		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
19369		* IERS Technical Note No. 32, BKG (2004)
19370		*
19371		*@version 2008 May 24
19372		*
19373		* @since Release 20101201
19374		*
19375		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19376		*/
19377		public static double jauSp00(double date1, double date2)
19378		{
19379		double t, sp;
19380
19381
19382		/* Interval between fundamental epoch J2000.0 and current date (JC). */
19383	34	t = ((date1 - DJ00) + date2) / DJC;
19384
19385		/* Approximate s'. */
19386	34	sp = -47e-6 * t * DAS2R;
19387
19388	34	return sp;
19389
19390		}
19391
19392
19393		/**
19394		* Star proper motion: update star catalog data for space motion.
19395		*
19396		*<p>This function is derived from the International Astronomical Union's
19397		* SOFA (Standards Of Fundamental Astronomy) software collection.
19398		*
19399		*<p>Status: support function.
19400		*
19401		*<!-- Given: -->
19402		* @param ra1 double right ascension (radians), before
19403		* @param dec1 double declination (radians), before
19404		* @param pmr1 double RA proper motion (radians/year), before
19405		* @param pmd1 double Dec proper motion (radians/year), before
19406		* @param px1 double parallax (arcseconds), before
19407		* @param rv1 double radial velocity (km/s, +ve = receding), before
19408		* @param ep1a double "before" epoch, part A (Note 1)
19409		* @param ep1b double "before" epoch, part B (Note 1)
19410		* @param ep2a double "after" epoch, part A (Note 1)
19411		* @param ep2b double "after" epoch, part B (Note 1)
19412		*
19413		*<!-- Returned: -->
19414		* @return ra2 double <u>returned</u> right ascension (radians), after
19415		* dec2 double <u>returned</u> declination (radians), after
19416		* pmr2 double <u>returned</u> RA proper motion (radians/year), after
19417		* pmd2 double <u>returned</u> Dec proper motion (radians/year), after
19418		* px2 double <u>returned</u> parallax (arcseconds), after
19419		* rv2 double <u>returned</u> radial velocity (km/s, +ve = receding), after
19420		*
19421		* <!-- Returned (function value): -->
19422		* @return int status:
19423		* -1 = system error (should not occur)
19424		* 0 = no warnings or errors
19425		* 1 = distance overridden (Note 6)
19426		* 2 = excessive velocity (Note 7)
19427		* 4 = solution didn't converge (Note 8)
19428		* else = binary logical OR of the above warnings
19429		*FIXME need to return the status as well.
19430		* <p>Notes:
19431		* <ol>
19432		*
19433		* <li> The starting and ending TDB dates ep1a+ep1b and ep2a+ep2b are
19434		* Julian Dates, apportioned in any convenient way between the two
19435		* parts (A and B). For example, JD(TDB)=2450123.7 could be
19436		* expressed in any of these ways, among others:
19437		*<pre>
19438		* epna epnb
19439		*
19440		* 2450123.7 0.0 (JD method)
19441		* 2451545.0 -1421.3 (J2000 method)
19442		* 2400000.5 50123.2 (MJD method)
19443		* 2450123.5 0.2 (date & time method)
19444		*</pre>
19445		* The JD method is the most natural and convenient to use in
19446		* cases where the loss of several decimal digits of resolution
19447		* is acceptable. The J2000 method is best matched to the way
19448		* the argument is handled internally and will deliver the
19449		* optimum resolution. The MJD method and the date & time methods
19450		* are both good compromises between resolution and convenience.
19451		*
19452		* <li> In accordance with normal star-catalog conventions, the object's
19453		* right ascension and declination are freed from the effects of
19454		* secular aberration. The frame, which is aligned to the catalog
19455		* equator and equinox, is Lorentzian and centered on the SSB.
19456		*
19457		* The proper motions are the rate of change of the right ascension
19458		* and declination at the catalog epoch and are in radians per TDB
19459		* Julian year.
19460		*
19461		* The parallax and radial velocity are in the same frame.
19462		*
19463		* <li> Care is needed with units. The star coordinates are in radians
19464		* and the proper motions in radians per Julian year, but the
19465		* parallax is in arcseconds.
19466		*
19467		* <li> The RA proper motion is in terms of coordinate angle, not true
19468		* angle. If the catalog uses arcseconds for both RA and Dec proper
19469		* motions, the RA proper motion will need to be divided by cos(Dec)
19470		* before use.
19471		*
19472		* <li> Straight-line motion at constant speed, in the inertial frame,
19473		* is assumed.
19474		*
19475		* <li> An extremely small (or zero or negative) parallax is interpreted
19476		* to mean that the object is on the "celestial sphere", the radius
19477		* of which is an arbitrary (large) value (see the jauStarpv
19478		* function for the value used). When the distance is overridden in
19479		* this way, the status, initially zero, has 1 added to it.
19480		*
19481		* <li> If the space velocity is a significant fraction of c (see the
19482		* constant VMAX in the function jauStarpv), it is arbitrarily set
19483		* to zero. When this action occurs, 2 is added to the status.
19484		*
19485		* <li> The relativistic adjustment carried out in the jauStarpv function
19486		* involves an iterative calculation. If the process fails to
19487		* converge within a set number of iterations, 4 is added to the
19488		* status.
19489		*</ol>
19490		*<p>Called:<ul>
19491		* <li>{@link #jauStarpv} star catalog data to space motion pv-vector
19492		* <li>{@link #jauPvu} update a pv-vector
19493		* <li>{@link #jauPdp} scalar product of two p-vectors
19494		* <li>{@link #jauPvstar} space motion pv-vector to star catalog data
19495		* </ul>
19496		*@version 2008 May 16
19497		*
19498		* @since Release 20101201
19499		*
19500		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19501		*/
19502		public static CatalogCoords jauStarpm(double ra1, double dec1,
19503		double pmr1, double pmd1, double px1, double rv1,
19504		double ep1a, double ep1b, double ep2a, double ep2b) throws JSOFAInternalError
19505		{
19506	4	double pv1[][] = new double[2][3], tl1, dt, pv[][] = new double[2][3], r2, rdv, v2, c2mv2, tl2,
19507	4	pv2[][] = new double[2][3];
19508	4	jauStarpv(ra1, dec1, pmr1, pmd1, px1, rv1, pv1);
19509
19510		/* Light time when observed (days). */
19511	4	tl1 = jauPm(pv1[0]) / DC;
19512
19513		/* Time interval, "before" to "after" (days). */
19514	4	dt = (ep2a - ep1a) + (ep2b - ep1b);
19515
19516		/* Move star along track from the "before" observed position to the */
19517		/* "after" geometric position. */
19518	4	pv = jauPvu(dt + tl1, pv1);
19519
19520		/* From this geometric position, deduce the observed light time (days) */
19521		/* at the "after" epoch (with theoretically unneccessary error check). */
19522	4	r2 = jauPdp(pv[0], pv[0]);
19523	4	rdv = jauPdp(pv[0], pv[1]);
19524	4	v2 = jauPdp(pv[1], pv[1]);
19525	4	c2mv2 = DC*DC - v2;
19526	4	if (c2mv2 <= 0) throw new JSOFAInternalError("internal error", -1);
19527	4	tl2 = (-rdv + sqrt(rdvrdv + c2mv2r2)) / c2mv2;
19528
19529		/* Move the position along track from the observed place at the */
19530		/* "before" epoch to the observed place at the "after" epoch. */
19531	4	pv2 =jauPvu(dt + (tl1 - tl2), pv1 );
19532
19533		/* Space motion pv-vector to RA,Dec etc. at the "after" epoch. */
19534	4	CatalogCoords cat = jauPvstar(pv2);
19535
19536	4	return cat;
19537
19538		}
19539
19540
19541		/**
19542		* Convert star catalog coordinates to position+velocity vector.
19543		*
19544		*<p>This function is derived from the International Astronomical Union's
19545		* SOFA (Standards Of Fundamental Astronomy) software collection.
19546		*
19547		*<p>Status: support function.
19548		*
19549		* Given (Note 1):
19550		* ra double right ascension (radians)
19551		* dec double declination (radians)
19552		* pmr double RA proper motion (radians/year)
19553		* pmd double Dec proper motion (radians/year)
19554		* px double parallax (arcseconds)
19555		* rv double radial velocity (km/s, positive = receding)
19556		*
19557		* Returned (Note 2):
19558		* pv double[2][3] pv-vector (AU, AU/day)
19559		*
19560		* <!-- Returned (function value): -->
19561		* @return int status:
19562		* 0 = no warnings
19563		* 1 = distance overridden (Note 6)
19564		* 2 = excessive speed (Note 7)
19565		* 4 = solution didn't converge (Note 8)
19566		* else = binary logical OR of the above
19567		*
19568		* <p>Notes:
19569		* <ol>
19570		*
19571		* <li> The star data accepted by this function are "observables" for an
19572		* imaginary observer at the solar-system barycenter. Proper motion
19573		* and radial velocity are, strictly, in terms of barycentric
19574		* coordinate time, TCB. For most practical applications, it is
19575		* permissible to neglect the distinction between TCB and ordinary
19576		* "proper" time on Earth (TT/TAI). The result will, as a rule, be
19577		* limited by the intrinsic accuracy of the proper-motion and
19578		* radial-velocity data; moreover, the pv-vector is likely to be
19579		* merely an intermediate result, so that a change of time unit
19580		* would cancel out overall.
19581		*
19582		* In accordance with normal star-catalog conventions, the object's
19583		* right ascension and declination are freed from the effects of
19584		* secular aberration. The frame, which is aligned to the catalog
19585		* equator and equinox, is Lorentzian and centered on the SSB.
19586		*
19587		* <li> The resulting position and velocity pv-vector is with respect to
19588		* the same frame and, like the catalog coordinates, is freed from
19589		* the effects of secular aberration. Should the "coordinate
19590		* direction", where the object was located at the catalog epoch, be
19591		* required, it may be obtained by calculating the magnitude of the
19592		* position vector pv[0][0-2] dividing by the speed of light in
19593		* AU/day to give the light-time, and then multiplying the space
19594		* velocity pv[1][0-2] by this light-time and adding the result to
19595		* pv[0][0-2].
19596		*
19597		* Summarizing, the pv-vector returned is for most stars almost
19598		* identical to the result of applying the standard geometrical
19599		* "space motion" transformation. The differences, which are the
19600		* subject of the Stumpff paper referenced below, are:
19601		*
19602		* (i) In stars with significant radial velocity and proper motion,
19603		* the constantly changing light-time distorts the apparent proper
19604		* motion. Note that this is a classical, not a relativistic,
19605		* effect.
19606		*
19607		* (ii) The transformation complies with special relativity.
19608		*
19609		* <li> Care is needed with units. The star coordinates are in radians
19610		* and the proper motions in radians per Julian year, but the
19611		* parallax is in arcseconds; the radial velocity is in km/s, but
19612		* the pv-vector result is in AU and AU/day.
19613		*
19614		* <li> The RA proper motion is in terms of coordinate angle, not true
19615		* angle. If the catalog uses arcseconds for both RA and Dec proper
19616		* motions, the RA proper motion will need to be divided by cos(Dec)
19617		* before use.
19618		*
19619		* <li> Straight-line motion at constant speed, in the inertial frame,
19620		* is assumed.
19621		*
19622		* <li> An extremely small (or zero or negative) parallax is interpreted
19623		* to mean that the object is on the "celestial sphere", the radius
19624		* of which is an arbitrary (large) value (see the constant PXMIN).
19625		* When the distance is overridden in this way, the status,
19626		* initially zero, has 1 added to it.
19627		*
19628		* <li> If the space velocity is a significant fraction of c (see the
19629		* constant VMAX), it is arbitrarily set to zero. When this action
19630		* occurs, 2 is added to the status.
19631		*
19632		* <li> The relativistic adjustment involves an iterative calculation.
19633		* If the process fails to converge within a set number (IMAX) of
19634		* iterations, 4 is added to the status.
19635		*
19636		* <li> The inverse transformation is performed by the function
19637		* jauPvstar.
19638		*</ol>
19639		*<p>Called:<ul>
19640		* <li>{@link #jauS2pv} spherical coordinates to pv-vector
19641		* <li>{@link #jauPm} modulus of p-vector
19642		* <li>{@link #jauZp} zero p-vector
19643		* <li>{@link #jauPn} decompose p-vector into modulus and direction
19644		* <li>{@link #jauPdp} scalar product of two p-vectors
19645		* <li>{@link #jauSxp} multiply p-vector by scalar
19646		* <li>{@link #jauPmp} p-vector minus p-vector
19647		* <li>{@link #jauPpp} p-vector plus p-vector
19648		* </ul>
19649		*<p>Reference:
19650		*
19651		* Stumpff, P., 1985, Astron.Astrophys. 144, 232-240.
19652		*
19653		*@version 2009 July 6
19654		*
19655		* @since Release 20101201
19656		*
19657		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19658		*/
19659		public static int jauStarpv(double ra, double dec,
19660		double pmr, double pmd, double px, double rv,
19661		double pv[][])
19662		{
19663		/* Smallest allowed parallax */
19664	10	final double PXMIN = 1e-7;
19665
19666		/* Largest allowed speed (fraction of c) */
19667	10	final double VMAX = 0.5;
19668
19669		/* Maximum number of iterations for relativistic solution */
19670	10	final int IMAX = 100;
19671
19672		int i, iwarn;
19673	10	double w, r, rd, rad, decd, v, x[] = new double[3], usr[] = new double[3], ust[] = new double[3],
19674		vsr, vst, betst, betsr, bett, betr,
19675	10	dd, ddel, ur[] = new double[3], ut[] = new double[3],
19676	10	d = 0.0, del = 0.0, /* to prevent */
19677	10	odd = 0.0, oddel = 0.0, /* compiler */
19678	10	od = 0.0, odel = 0.0; /* warnings */
19679
19680
19681		/* Distance (AU). */
19682	10	if (px >= PXMIN) {
19683	10	w = px;
19684	10	iwarn = 0;
19685		} else {
19686	0	w = PXMIN;
19687	0	iwarn = 1;
19688		}
19689	10	r = DR2AS / w;
19690
19691		/* Radial velocity (AU/day). */
19692	10	rd = DAYSEC * rv * 1e3 / DAU;
19693
19694		/* Proper motion (radian/day). */
19695	10	rad = pmr / DJY;
19696	10	decd = pmd / DJY;
19697
19698		/* To pv-vector (AU,AU/day). */
19699	10	double[][] pvt = jauS2pv(ra, dec, r, rad, decd, rd);
19700	10	jauCpv(pvt,pv);
19701
19702		/* If excessive velocity, arbitrarily set it to zero. */
19703	10	v = jauPm(pv[1]);
19704	10	if (v / DC > VMAX) {
19705	0	jauZp(pv[1]);
19706	0	iwarn += 2;
19707		}
19708
19709		/* Isolate the radial component of the velocity (AU/day). */
19710	10	NormalizedVector nv = jauPn(pv[0]);
19711	10	w = nv.r;
19712	10	x = nv.u;
19713	10	vsr = jauPdp(x, pv[1]);
19714	10	usr = jauSxp(vsr,x);
19715
19716		/* Isolate the transverse component of the velocity (AU/day). */
19717	10	ust = jauPmp(pv[1], usr);
19718	10	vst = jauPm(ust);
19719
19720		/* Special-relativity dimensionless parameters. */
19721	10	betsr = vsr / DC;
19722	10	betst = vst / DC;
19723
19724		/* Determine the inertial-to-observed relativistic correction terms. */
19725	10	bett = betst;
19726	10	betr = betsr;
19727	56	for (i = 0; i < IMAX; i++) {
19728	56	d = 1.0 + betr;
19729	56	del = sqrt(1.0 - betrbetr - bettbett) - 1.0;
19730	56	betr = d * betsr + del;
19731	56	bett = d * betst;
19732	56	if (i > 0) {
19733	46	dd = abs(d - od);
19734	46	ddel = abs(del - odel);
19735	46	if ((i > 1) && (dd >= odd) && (ddel >= oddel)) break;
19736	36	odd = dd;
19737	36	oddel = ddel;
19738		}
19739	46	od = d;
19740	46	odel = del;
19741		}
19742	10	if (i >= IMAX) iwarn += 4;
19743
19744		/* Replace observed radial velocity with inertial value. */
19745	10	w = (betsr != 0.0) ? d + del / betsr : 1.0;
19746	10	ur = jauSxp(w,usr);
19747
19748		/* Replace observed tangential velocity with inertial value. */
19749	10	ut = jauSxp(d,ust);
19750
19751		/* Combine the two to obtain the inertial space velocity. */
19752	10	pv[1] = jauPpp(ur, ut);
19753
19754		/* Return the status. */
19755	10	return iwarn;
19756
19757		}
19758
19759
19760		/**
19761		* Multiply a p-vector by a scalar.
19762		*
19763		*<p>This function is derived from the International Astronomical Union's
19764		* SOFA (Standards Of Fundamental Astronomy) software collection.
19765		*
19766		*<p>Status: vector/matrix support function.
19767		*
19768		*<!-- Given: -->
19769		* @param s double scalar
19770		* @param p double[3] p-vector
19771		*
19772		*<!-- Returned: -->
19773		* @return sp double[3] <u>returned</u> s * p
19774		*
19775		*
19776		*
19777		*@version 2008 October 28
19778		*
19779		* @since Release 20101201
19780		*
19781		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19782		*/
19783		public static double[] jauSxp(double s, double p[])
19784		{
19785	254	double sp[] = new double[3];
19786	254	sp[0] = s * p[0];
19787	254	sp[1] = s * p[1];
19788	254	sp[2] = s * p[2];
19789
19790	254	return sp;
19791
19792		}
19793
19794
19795		/**
19796		* Multiply a pv-vector by a scalar.
19797		*
19798		*<p>This function is derived from the International Astronomical Union's
19799		* SOFA (Standards Of Fundamental Astronomy) software collection.
19800		*
19801		*<p>Status: vector/matrix support function.
19802		*
19803		*<!-- Given: -->
19804		* @param s double scalar
19805		* @param pv double[2][3] pv-vector
19806		*
19807		*<!-- Returned: -->
19808		* @return spv double[2][3] <u>returned</u> s * pv
19809		*
19810		* Note:
19811		* It is permissible for pv and psv to be the same array
19812		*
19813		*<p>Called:<ul>
19814		* <li>{@link #jauS2xpv} multiply pv-vector by two scalars
19815		* </ul>
19816		*@version 2008 October 28
19817		*
19818		* @since Release 20101201
19819		*
19820		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
19821		*/
19822		public static double[][] jauSxpv(double s, double pv[][])
19823		{
19824		double spv[][];
19825	2	spv = jauS2xpv(s, s, pv);
19826
19827	2	return spv;
19828
19829		}
19830
19831		/**
19832		*
19833		* Time scale transformation: International Atomic Time, TAI, to
19834		* Terrestrial Time, TT.
19835		*
19836		* <p>This function is derived from the International Astronomical Union's
19837		* SOFA (Standards of Fundamental Astronomy) software collection.
19838		*
19839		*<p>Status: canonical.
19840		*
19841		*<!-- Given: -->
19842		* @param tai1 double TAI as a 2-part Julian Date
19843		* @param tai2 double TAI as a 2-part Julian Date
19844		*
19845		*<!-- Returned:-->
19846		* @return JulianDate TT as a 2-part Julian Date
19847		*
19848		*
19849		* Note:
19850		*
19851		* tai1+tai2 is Julian Date, apportioned in any convenient way
19852		* between the two arguments, for example where tai1 is the Julian
19853		* Day Number and tai2 is the fraction of a day. The returned
19854		* tt1,tt2 follow suit.
19855		*
19856		*<p>References:
19857		*
19858		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
19859		* IERS Technical Note No. 32, BKG (2004)
19860		*
19861		* Explanatory Supplement to the Astronomical Almanac,
19862		* P. Kenneth Seidelmann (ed), University Science Books (1992)
19863		*
19864		*@version 2010 May 16
19865		*
19866		*@since SOFA release 2010-12-01
19867		*
19868		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
19869		*/
19870		public static JulianDate jauTaitt(double tai1, double tai2)
19871		{
19872
19873		double tt1, tt2;
19874		/* TT minus TAI (days). */
19875	26	final double dtat = TTMTAI / DAYSEC;
19876
19877		/* Result, safeguarding precision. */
19878
19879	26	if ( tai1 > tai2 ) {
19880	26	tt1 = tai1;
19881	26	tt2 = tai2 + dtat;
19882		} else {
19883	0	tt1 = tai1 + dtat;
19884	0	tt2 = tai2;
19885		}
19886
19887
19888	26	return new JulianDate(tt1, tt2);
19889		};
19890
19891		/**
19892		*
19893		* Time scale transformation: International Atomic Time, TAI, to
19894		* Universal Time, UT1.
19895		*
19896		* <p>This function is derived from the International Astronomical Union's
19897		* SOFA (Standards of Fundamental Astronomy) software collection.
19898		*
19899		*<p>Status: canonical.
19900		*
19901		*<!-- Given: -->
19902		* @param tai1 double TAI as a 2-part Julian Date
19903		* @param tai2 double TAI as a 2-part Julian Date
19904		* @param dta double UT1-TAI in seconds
19905		*
19906		*<!-- Returned:-->
19907		* @return UT1 as a 2-part Julian Date
19908		*
19909		*
19910		*<p>Notes:
19911		* <ol>
19912		* <li> tai1+tai2 is Julian Date, apportioned in any convenient way
19913		* between the two arguments, for example where tai1 is the Julian
19914		* Day Number and tai2 is the fraction of a day. The returned
19915		* UT11,UT12 follow suit.
19916		*
19917		* <li> The argument dta, i.e. UT1-TAI, is an observed quantity, and is
19918		* available from IERS tabulations.
19919		* </ol>
19920		* Reference:
19921		*
19922		* Explanatory Supplement to the Astronomical Almanac,
19923		* P. Kenneth Seidelmann (ed), University Science Books (1992)
19924		*
19925		*@version 2010 May 16
19926		*
19927		*@since SOFA release 2010-12-01
19928		*
19929		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
19930		*
19931		*/
19932		public static JulianDate jauTaiut1(double tai1, double tai2, double dta)
19933
19934		{
19935		double dtad,ut11, ut12;
19936
19937
19938		/* Result, safeguarding precision. */
19939	28	dtad = dta / DAYSEC;
19940	28	if ( tai1 > tai2 ) {
19941	28	ut11 = tai1;
19942	28	ut12 = tai2 + dtad;
19943		} else {
19944	0	ut11 = tai1 + dtad;
19945	0	ut12 = tai2;
19946		}
19947
19948	28	return new JulianDate(ut11, ut12);
19949		};
19950
19951		/**
19952		*
19953		* Time scale transformation: International Atomic Time, TAI, to
19954		* Coordinated Universal Time, UTC.
19955		*
19956		* <p>This function is derived from the International Astronomical Union's
19957		* SOFA (Standards of Fundamental Astronomy) software collection.
19958		*
19959		*<p>Status: canonical.
19960		*
19961		*<!-- Given: -->
19962		* @param tai1 TAI as a 2-part Julian Date (Note 1)
19963		* @param tai2 TAI as a 2-part Julian Date (Note 1)
19964		*
19965		*<!-- Returned:-->
19966		* @return UTC as a 2-part quasi Julian Date (Notes 1-3)
19967		*
19968		* Returned (function value):
19969		* int status: +1 = dubious year (Note 4)
19970		* 0 = OK
19971		* -1 = unacceptable date
19972		*
19973		*<p>Notes:</p>
19974		* <ol>
19975		* <li> tai1+tai2 is Julian Date, apportioned in any convenient way
19976		* between the two arguments, for example where tai1 is the Julian
19977		* Day Number and tai2 is the fraction of a day. The returned utc1
19978		* and utc2 form an analogous pair, except that a special convention
19979		* is used, to deal with the problem of leap seconds - see the next
19980		* note.
19981		*
19982		* <li> JD cannot unambiguously represent UTC during a leap second unless
19983		* special measures are taken. The convention in the present
19984		* function is that the JD day represents UTC days whether the
19985		* length is 86399, 86400 or 86401 SI seconds.
19986		*
19987		* <li> The function jauD2dtf can be used to transform the UTC quasi-JD
19988		* into calendar date and clock time, including UTC leap second
19989		* handling.
19990		*
19991		* <li> The warning status "dubious year" flags UTCs that predate the
19992		* introduction of the time scale and that are too far in the future
19993		* to be trusted. See jauDat for further details.
19994		* </ol>
19995		* Called:
19996		* <ul>
19997		* <li>{@link #jauJd2cal} JD to Gregorian calendar
19998		* <li>{@link #jauDat} delta(AT) = TAI-UTC
19999		* <li>{@link #jauCal2jd} Gregorian calendar to JD
20000		*</ul>
20001		*<p>References:
20002		*
20003		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
20004		* IERS Technical Note No. 32, BKG (2004)
20005		*
20006		* Explanatory Supplement to the Astronomical Almanac,
20007		* P. Kenneth Seidelmann (ed), University Science Books (1992)
20008		*
20009		*@version 2010 May 16
20010		*
20011		*@since SOFA release 2010-12-01
20012		*
20013		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20014		* @throws JSOFAIllegalParameter
20015		* @throws JSOFAInternalError
20016		*/
20017		public static JulianDate jauTaiutc(double tai1, double tai2) throws JSOFAIllegalParameter, JSOFAInternalError
20018		{
20019		boolean big1;
20020		int i;
20021	2	double a1, a2,dats1, ddats, dats2, datd = 0.0, as1, as2, da, d1, d2, fd;
20022		double utc1, utc2;
20023
20024
20025		/* Put the two parts of the TAI into big-first order. */
20026	2	big1 = ( tai1 >= tai2 );
20027	2	if ( big1 ) {
20028	2	a1 = tai1;
20029	2	a2 = tai2;
20030		} else {
20031	0	a1 = tai2;
20032	0	a2 = tai1;
20033		}
20034
20035		/* See if the TAI can possibly be in a leap-second day. */
20036	2	d1 = a1;
20037	2	dats1 = 0.0;
20038	12	for ( i = -1; i <= 3; i++ ) {
20039	10	d2 = a2 + (double) i;
20040		Calendar dt;
20041	10	dt = jauJd2cal(d1, d2 );
20042	10	dats2 = jauDat(dt.iy, dt.im, dt.id, 0.0);
20043		//FIXME if ( js < 0 ) return -1;
20044	10	if ( i == -1 ) dats1 = dats2;
20045	10	ddats = dats2 - dats1;
20046	10	datd = dats1 / DAYSEC;
20047	10	if ( abs(ddats) >= 0.5 ) {
20048
20049		/* Yes. Get TAI for the start of the UTC day that */
20050		/* ends in a leap. */
20051	0	JulianDate jd = jauCal2jd(dt.iy, dt.im, dt.id );
20052	0	d1 = jd.djm0; d2 = jd.djm1;
20053	0	as1 = d1;
20054	0	as2 = d2 - 1.0 + datd;
20055
20056		/* Is the TAI after this point? */
20057	0	da = a1 - as1;
20058	0	da = da + ( a2 - as2 );
20059	0	if ( da > 0 ) {
20060
20061		/* Yes: fraction of the current UTC day that has elapsed. */
20062	0	fd = da * DAYSEC / ( DAYSEC + ddats );
20063
20064		/* Ramp TAI-UTC to bring about SOFA's JD(UTC) convention. */
20065	0	datd += ddats * ( fd <= 1.0 ? fd : 1.0 ) / DAYSEC;
20066		}
20067
20068		/* Done. */
20069		break;
20070		}
20071	10	dats1 = dats2;
20072		}
20073
20074		/* Subtract the (possibly adjusted) TAI-UTC from TAI to give UTC. */
20075	2	a2 -= datd;
20076
20077		/* Return the UTC result, preserving the TAI order. */
20078	2	if ( big1 ) {
20079	2	utc1 = a1;
20080	2	utc2 = a2;
20081		} else {
20082	0	utc1 = a2;
20083	0	utc2 = a1;
20084		}
20085
20086		/* TODO Status */
20087	2	return new JulianDate(utc1, utc2);
20088
20089		};
20090
20091		/**
20092		*
20093		* Time scale transformation: Barycentric Coordinate Time, TCB, to
20094		* Barycentric Dynamical Time, TDB.
20095		*
20096		* <p>This function is derived from the International Astronomical Union's
20097		* SOFA (Standards of Fundamental Astronomy) software collection.
20098		*
20099		*<p>Status: canonical.
20100		*
20101		*<!-- Given: -->
20102		* @param tcb1 double TCB as a 2-part Julian Date
20103		* @param tcb2 double TCB as a 2-part Julian Date
20104		*
20105		*<!-- Returned:-->
20106		* @return TDB as a 2-part Julian Date
20107		*
20108		*
20109		*<p>Notes:
20110		* <ol>
20111		* <li> tcb1+tcb2 is Julian Date, apportioned in any convenient way
20112		* between the two arguments, for example where tcb1 is the Julian
20113		* Day Number and tcb2 is the fraction of a day. The returned
20114		* tdb1,tdb2 follow suit.
20115		*
20116		* <li> The 2006 IAU General Assembly introduced a conventional linear
20117		* transformation between TDB and TCB. This transformation
20118		* compensates for the drift between TCB and terrestrial time TT,
20119		* and keeps TDB approximately centered on TT. Because the
20120		* relationship between TT and TCB depends on the adopted solar
20121		* system ephemeris, the degree of alignment between TDB and TT over
20122		* long intervals will vary according to which ephemeris is used.
20123		* Former definitions of TDB attempted to avoid this problem by
20124		* stipulating that TDB and TT should differ only by periodic
20125		* effects. This is a good description of the nature of the
20126		* relationship but eluded precise mathematical formulation. The
20127		* conventional linear relationship adopted in 2006 sidestepped
20128		* these difficulties whilst delivering a TDB that in practice was
20129		* consistent with values before that date.
20130		*
20131		* <li> TDB is essentially the same as Teph, the time argument for the
20132		* JPL solar system ephemerides.
20133		* </ol>
20134		* Reference:
20135		*
20136		* IAU 2006 Resolution B3
20137		*
20138		*@version 2010 May 16
20139		*
20140		*@since SOFA release 2010-12-01
20141		*
20142		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20143		*/
20144		public static JulianDate jauTcbtdb(double tcb1, double tcb2)
20145		{
20146		double tdb1, tdb2;
20147		/* 1977 Jan 1 00:00:32.184 TT, as two-part JD */
20148	2	final double t77td = DJM0 + DJM77;
20149	2	final double t77tf = TTMTAI/DAYSEC;
20150
20151		/* TDB (days) at TAI 1977 Jan 1.0 */
20152	2	final double tdb0 = TDB0/86400.0;
20153
20154		double d;
20155
20156
20157		/* Result, safeguarding precision. */
20158	2	if ( tcb1 > tcb2 ) {
20159	2	d = tcb1 - t77td;
20160	2	tdb1 = tcb1;
20161	2	tdb2 = tcb2 + tdb0 - ( d + ( tcb2 - t77tf ) ) * ELB;
20162		} else {
20163	0	d = tcb2 - t77td;
20164	0	tdb1 = tcb1 + tdb0 - ( d + ( tcb1 - t77tf ) ) * ELB;
20165	0	tdb2 = tcb2;
20166		}
20167
20168
20169	2	return new JulianDate(tdb1, tdb2);
20170
20171		};
20172
20173		/**
20174		* Time scale transformation: Geocentric Coordinate Time, TCG, to
20175		* Terrestrial Time, TT.
20176		*
20177		* <p>This function is derived from the International Astronomical Union's
20178		* SOFA (Standards of Fundamental Astronomy) software collection.
20179		*
20180		*<p>Status: canonical.
20181		*
20182		*<!-- Given: -->
20183		* @param tcg1 double TCG as a 2-part Julian Date
20184		* @param tcg2 double TCG as a 2-part Julian Date
20185		*
20186		*<!-- Returned:-->
20187		* @return TT as a 2-part Julian Date
20188		*
20189		*
20190		* Note:
20191		*
20192		* tcg1+tcg2 is Julian Date, apportioned in any convenient way
20193		* between the two arguments, for example where tcg1 is the Julian
20194		* Day Number and tcg22 is the fraction of a day. The returned
20195		* tt1,tt2 follow suit.
20196		*
20197		*<p>References:
20198		*
20199		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),.
20200		* IERS Technical Note No. 32, BKG (2004)
20201		*
20202		* IAU 2000 Resolution B1.9
20203		*
20204		*@version 2010 May 14
20205		*
20206		*@since SOFA release 2010-12-01
20207		*
20208		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20209		*/
20210		public static JulianDate jauTcgtt(double tcg1, double tcg2)
20211		{
20212		double tt1,tt2;
20213		/* 1977 Jan 1 00:00:32.184 TT, as MJD */
20214	2	final double t77t = DJM77 + TTMTAI/DAYSEC;
20215
20216
20217		/* Result, safeguarding precision. */
20218	2	if ( tcg1 > tcg2 ) {
20219	2	tt1 = tcg1;
20220	2	tt2 = tcg2 - ( ( tcg1 - DJM0 ) + ( tcg2 - t77t ) ) * ELG;
20221		} else {
20222	0	tt1 = tcg1 - ( ( tcg2 - DJM0 ) + ( tcg1 - t77t ) ) * ELG;
20223	0	tt2 = tcg2;
20224		}
20225
20226	2	return new JulianDate(tt1, tt2);
20227		};
20228
20229
20230		/**
20231		*
20232		* Time scale transformation: Barycentric Dynamical Time, TDB, to
20233		* Barycentric Coordinate Time, TCB.
20234		*
20235		* <p>This function is derived from the International Astronomical Union's
20236		* SOFA (Standards of Fundamental Astronomy) software collection.
20237		*
20238		*<p>Status: canonical.
20239		*
20240		*<!-- Given: -->
20241		* @param tdb1 TDB as a 2-part Julian Date
20242		* @param tdb2 TDB as a 2-part Julian Date
20243		*
20244		*<!-- Returned:-->
20245		* @return TCB as a 2-part Julian Date
20246		*
20247		*<p>Notes:
20248		* <ol>
20249		* <li> tdb1+tdb2 is Julian Date, apportioned in any convenient way
20250		* between the two arguments, for example where tdb1 is the Julian
20251		* Day Number and tdb2 is the fraction of a day. The returned
20252		* tcb1,tcb2 follow suit.
20253		*
20254		* <li> The 2006 IAU General Assembly introduced a conventional linear
20255		* transformation between TDB and TCB. This transformation
20256		* compensates for the drift between TCB and terrestrial time TT,
20257		* and keeps TDB approximately centered on TT. Because the
20258		* relationship between TT and TCB depends on the adopted solar
20259		* system ephemeris, the degree of alignment between TDB and TT over
20260		* long intervals will vary according to which ephemeris is used.
20261		* Former definitions of TDB attempted to avoid this problem by
20262		* stipulating that TDB and TT should differ only by periodic
20263		* effects. This is a good description of the nature of the
20264		* relationship but eluded precise mathematical formulation. The
20265		* conventional linear relationship adopted in 2006 sidestepped
20266		* these difficulties whilst delivering a TDB that in practice was
20267		* consistent with values before that date.
20268		*
20269		* <li> TDB is essentially the same as Teph, the time argument for the
20270		* JPL solar system ephemerides.
20271		* </ol>
20272		* Reference:
20273		*
20274		* IAU 2006 Resolution B3
20275		*
20276		*@version 2010 September 10
20277		*
20278		*@since SOFA release 2010-12-01
20279		*
20280		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20281		*/
20282		public static JulianDate jauTdbtcb(double tdb1, double tdb2 )
20283		{
20284		double tcb1, tcb2;
20285		/* 1977 Jan 1 00:00:32.184 TT, as two-part JD */
20286	2	final double t77td = DJM0 + DJM77;
20287	2	final double t77tf = TTMTAI/DAYSEC;
20288
20289		/* TDB (days) at TAI 1977 Jan 1.0 */
20290	2	final double tdb0 = TDB0/DAYSEC;
20291
20292		/* TDB to TCB rate */
20293	2	final double elbb = ELB/(1.0-ELB);
20294
20295		double d, f;
20296
20297
20298		/* Result, preserving date format but safeguarding precision. */
20299	2	if ( tdb1 > tdb2 ) {
20300	2	d = t77td - tdb1;
20301	2	f = tdb2 - tdb0;
20302	2	tcb1 = tdb1;
20303	2	tcb2 = f - ( d - ( f - t77tf ) ) * elbb;
20304		} else {
20305	0	d = t77td - tdb2;
20306	0	f = tdb1 - tdb0;
20307	0	tcb1 = f + ( d - ( f - t77tf ) ) * elbb;
20308	0	tcb2 = tdb2;
20309		}
20310
20311	2	return new JulianDate(tcb1, tcb2);
20312
20313		};
20314
20315
20316		/**
20317		*
20318		* Time scale transformation: Barycentric Dynamical Time, TDB, to
20319		* Terrestrial Time, TT.
20320		*
20321		* <p>This function is derived from the International Astronomical Union's
20322		* SOFA (Standards of Fundamental Astronomy) software collection.
20323		*
20324		*<p>Status: canonical.
20325		*
20326		*<!-- Given: -->
20327		* @param tdb1 double TDB as a 2-part Julian Date
20328		* @param tdb2 double TDB as a 2-part Julian Date
20329		* @param dtr double TDB-TT in seconds
20330		*
20331		*<!-- Returned:-->
20332		* @return TT as a 2-part Julian Date
20333		*
20334		*
20335		*<p>Notes:
20336		* <ol>
20337		* <li> tdb1+tdb2 is Julian Date, apportioned in any convenient way
20338		* between the two arguments, for example where tdb1 is the Julian
20339		* Day Number and tdb2 is the fraction of a day. The returned
20340		* tt1,tt2 follow suit.
20341		*
20342		* <li> The argument dtr represents the quasi-periodic component of the
20343		* GR transformation between TT and TCB. It is dependent upon the
20344		* adopted solar-system ephemeris, and can be obtained by numerical
20345		* integration, by interrogating a precomputed time ephemeris or by
20346		* evaluating a model such as that implemented in the SOFA function
20347		* jauDtdb. The quantity is dominated by an annual term of 1.7 ms
20348		* amplitude.
20349		*
20350		* <li> TDB is essentially the same as Teph, the time argument for the
20351		* JPL solar system ephemerides.
20352		* </ol>
20353		*<p>References:
20354		*
20355		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
20356		* IERS Technical Note No. 32, BKG (2004)
20357		*
20358		* IAU 2006 Resolution 3
20359		*
20360		*@version 2010 May 13
20361		*
20362		*@since SOFA release 2010-12-01
20363		*
20364		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20365		*
20366		*/
20367		public static JulianDate jauTdbtt(double tdb1, double tdb2, double dtr )
20368		{
20369		double tt1, tt2;
20370		double dtrd;
20371
20372
20373		/* Result, safeguarding precision. */
20374	2	dtrd = dtr / DAYSEC;
20375	2	if ( tdb1 > tdb2 ) {
20376	2	tt1 = tdb1;
20377	2	tt2 = tdb2 - dtrd;
20378		} else {
20379	0	tt1 = tdb1 - dtrd;
20380	0	tt2 = tdb2;
20381		}
20382
20383	2	return new JulianDate(tt1, tt2);
20384
20385		}
20386
20387		/**
20388		*
20389		* Convert hours, minutes, seconds to radians.
20390		*
20391		* <p>This function is derived from the International Astronomical Union's
20392		* SOFA (Standards of Fundamental Astronomy) software collection.
20393		*
20394		*<p>Status: support function.
20395		*
20396		*<!-- Given: -->
20397		* @param s char sign: '-' = negative, otherwise positive
20398		* @param ihour int hours
20399		* @param imin int minutes
20400		* @param sec double seconds
20401		*
20402		*<!-- Returned:-->
20403		* @return double angle in radians
20404		*@throws JSOFAIllegalParameter illegal parameter of some form
20405		* Returned (function value):
20406		* int status: 0 = OK
20407		* 1 = ihour outside range 0-23
20408		* 2 = imin outside range 0-59
20409		* 3 = sec outside range 0-59.999...
20410		*
20411		*<p>Notes:
20412		*<ul>
20413		* <li> The result is computed even if any of the range checks fail.
20414		*
20415		* <li> Negative ihour, imin and/or sec produce a warning status, but
20416		* the absolute value is used in the conversion.
20417		*</ul>
20418		*@version 2010 August 27
20419		*
20420		*@since SOFA release 2010-12-01
20421		*
20422		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20423		*
20424		*/
20425		public static double jauTf2a(char s, int ihour, int imin, double sec ) throws JSOFAIllegalParameter
20426		{
20427		double rad;
20428
20429		/* Compute the interval. */
20430	0	rad = ( s == '-' ? -1.0 : 1.0 ) *
20431	0	( 60.0 * ( 60.0 * ( (double) abs(ihour) ) +
20432	0	( (double) abs(imin) ) ) +
20433	0	abs(sec) ) * DS2R;
20434
20435		/* Validate arguments and return status. */
20436	0	if ( ihour < 0 \|\| ihour > 23 ) throw new JSOFAIllegalParameter("bad hour", 1);
20437	0	if ( imin < 0 \|\| imin > 59 ) throw new JSOFAIllegalParameter("bad minute", 2);
20438	0	if ( sec < 0.0 \|\| sec >= 60.0 )throw new JSOFAIllegalParameter("bad second", 3);
20439	0	return rad;
20440
20441		};
20442
20443		/**
20444		*
20445		* Convert hours, minutes, seconds to days.
20446		*
20447		* <p>This function is derived from the International Astronomical Union's
20448		* SOFA (Standards of Fundamental Astronomy) software collection.
20449		*
20450		*<p>Status: support function.
20451		*
20452		*<!-- Given: -->
20453		* @param s char sign: '-' = negative, otherwise positive
20454		* @param ihour int hours
20455		* @param imin int minutes
20456		* @param sec double seconds
20457		*
20458		*<!-- Returned:-->
20459		* days double interval in days
20460		*
20461		* Returned (function value):
20462		* int status: 0 = OK
20463		* 1 = ihour outside range 0-23
20464		* 2 = imin outside range 0-59
20465		* 3 = sec outside range 0-59.999...
20466		*
20467		*<p>Notes:
20468		*<ol>
20469		* <li> The result is computed even if any of the range checks fail.
20470		*
20471		* <li> Negative ihour, imin and/or sec produce a warning status, but
20472		* the absolute value is used in the conversion.
20473		*</ol>
20474		*@version 2010 August 27
20475		*
20476		*@since SOFA release 2010-12-01
20477		*
20478		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
20479		* @throws JSOFAIllegalParameter
20480		*/
20481		public static double jauTf2d(char s, int ihour, int imin, double sec) throws JSOFAIllegalParameter
20482		{
20483		double days;
20484		/* Compute the interval. */
20485	0	days = ( s == '-' ? -1.0 : 1.0 ) *
20486	0	( 60.0 * ( 60.0 * ( (double) abs(ihour) ) +
20487	0	( (double) abs(imin) ) ) +
20488	0	abs(sec) ) / DAYSEC;
20489
20490		/* FIXME Validate arguments and return status. */
20491	0	if ( ihour < 0 \|\| ihour > 23 ) throw new JSOFAIllegalParameter("bad hour", 1);
20492	0	if ( imin < 0 \|\| imin > 59 ) throw new JSOFAIllegalParameter("bad minute", 2);
20493	0	if ( sec < 0.0 \|\| sec >= 60.0 ) throw new JSOFAIllegalParameter("bad second", 3);
20494	0	return days;
20495
20496		}
20497
20498		/**
20499		* Transpose an r-matrix.
20500		*
20501		*<p>This function is derived from the International Astronomical Union's
20502		* SOFA (Standards Of Fundamental Astronomy) software collection.
20503		*
20504		*<p>Status: vector/matrix support function.
20505		*
20506		*<!-- Given: -->
20507		* @param r double[3][3] r-matrix
20508		*
20509		*<!-- Returned: -->
20510		* @return rt double[3][3] <u>returned</u> transpose
20511		*
20512		* Note:
20513		* It is permissible for r and rt to be the same array.
20514		*
20515		*<p>Called:<ul>
20516		* <li>{@link #jauCr} copy r-matrix
20517		* </ul>
20518		*@version 2008 May 22
20519		*
20520		* @since Release 20101201
20521		*
20522		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
20523		*/
20524		public static double[][] jauTr(double r[][])
20525		{
20526	86	double wm[][]= new double[3][3];
20527		int i, j;
20528
20529
20530	344	for (i = 0; i < 3; i++) {
20531	1032	for (j = 0; j < 3; j++) {
20532	774	wm[i][j] = r[j][i];
20533		}
20534		}
20535
20536
20537	86	return wm;
20538
20539		}
20540
20541
20542		/**
20543		* Multiply a p-vector by the transpose of an r-matrix.
20544		*
20545		*<p>This function is derived from the International Astronomical Union's
20546		* SOFA (Standards Of Fundamental Astronomy) software collection.
20547		*
20548		*<p>Status: vector/matrix support function.
20549		*
20550		*<!-- Given: -->
20551		* @param r double[3][3] r-matrix
20552		* @param p double[3] p-vector
20553		*
20554		*<!-- Returned: -->
20555		* @return trp double[3] <u>returned</u> r * p
20556		*
20557		* Note:
20558		* It is permissible for p and trp to be the same array.
20559		*
20560		*<p>Called:<ul>
20561		* <li>{@link #jauTr} transpose r-matrix
20562		* <li>{@link #jauRxp} product of r-matrix and p-vector
20563		* </ul>
20564		*@version 2008 October 28
20565		*
20566		* @since Release 20101201
20567		*
20568		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
20569		*/
20570		public static double[] jauTrxp(double r[][], double p[] )
20571		{
20572		double tr[][];
20573		double trp[];
20574
20575		/* Transpose of matrix r. */
20576	60	tr = jauTr(r);
20577
20578		/* Matrix tr * vector p -> vector trp. */
20579	60	trp = jauRxp(tr, p);
20580
20581	60	return trp;
20582
20583		}
20584
20585
20586		/**
20587		* Multiply a pv-vector by the transpose of an r-matrix.
20588		*
20589		*<p>This function is derived from the International Astronomical Union's
20590		* SOFA (Standards Of Fundamental Astronomy) software collection.
20591		*
20592		*<p>Status: vector/matrix support function.
20593		*
20594		*<!-- Given: -->
20595		* @param r double[3][3] r-matrix
20596		* @param pv double[2][3] pv-vector
20597		*
20598		*<!-- Returned: -->
20599		* @return trpv double[2][3] <u>returned</u> r * pv
20600		*
20601		* Note:
20602		* It is permissible for pv and trpv to be the same array.
20603		*
20604		*<p>Called:<ul>
20605		* <li>{@link #jauTr} transpose r-matrix
20606		* <li>{@link #jauRxpv} product of r-matrix and pv-vector
20607		* </ul>
20608		*@version 2008 October 28
20609		*
20610		* @since Release 20101201
20611		*
20612		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
20613		*/
20614		public static double[][] jauTrxpv(double r[][], double pv[][] )
20615		{
20616		double tr[][], trpv[][];
20617
20618
20619		/* Transpose of matrix r. */
20620	14	tr = jauTr(r);
20621
20622		/* Matrix tr * vector pv -> vector trpv. */
20623	14	trpv = jauRxpv(tr, pv);
20624
20625	14	return trpv;
20626
20627		}
20628
20629		/*
20630		* constant arrays set outside jauXy06 to avoid problems with 65535 byte limit on function size
20631		*/
20632		static {
20633		/* need to define this function because it appears that javac lumps all of the statically defined initalizers into one function on
20634		* compilation - so this will force a second function */
20635	2	init_mfals();
20636		}
20637		/** Fundamental-argument multipliers: luni-solar terms */
20638		private static int mfals[][]; //IMPL would like to be final really
20639
20640		private static void init_mfals(){
20641
20642	2	mfals = new int[][]
20643		{
20644
20645		/* 1-10 */
20646		{ 0, 0, 0, 0, 1 },
20647		{ 0, 0, 2, -2, 2 },
20648		{ 0, 0, 2, 0, 2 },
20649		{ 0, 0, 0, 0, 2 },
20650		{ 0, 1, 0, 0, 0 },
20651		{ 0, 1, 2, -2, 2 },
20652		{ 1, 0, 0, 0, 0 },
20653		{ 0, 0, 2, 0, 1 },
20654		{ 1, 0, 2, 0, 2 },
20655		{ 0, 1, -2, 2, -2 },
20656
20657		/* 11-20 */
20658		{ 0, 0, 2, -2, 1 },
20659		{ 1, 0, -2, 0, -2 },
20660		{ 1, 0, 0, -2, 0 },
20661		{ 1, 0, 0, 0, 1 },
20662		{ 1, 0, 0, 0, -1 },
20663		{ 1, 0, -2, -2, -2 },
20664		{ 1, 0, 2, 0, 1 },
20665		{ 2, 0, -2, 0, -1 },
20666		{ 0, 0, 0, 2, 0 },
20667		{ 0, 0, 2, 2, 2 },
20668
20669		/* 21-30 */
20670		{ 2, 0, 0, -2, 0 },
20671		{ 0, 2, -2, 2, -2 },
20672		{ 2, 0, 2, 0, 2 },
20673		{ 1, 0, 2, -2, 2 },
20674		{ 1, 0, -2, 0, -1 },
20675		{ 2, 0, 0, 0, 0 },
20676		{ 0, 0, 2, 0, 0 },
20677		{ 0, 1, 0, 0, 1 },
20678		{ 1, 0, 0, -2, -1 },
20679		{ 0, 2, 2, -2, 2 },
20680
20681		/* 31-40 */
20682		{ 0, 0, 2, -2, 0 },
20683		{ 1, 0, 0, -2, 1 },
20684		{ 0, 1, 0, 0, -1 },
20685		{ 0, 2, 0, 0, 0 },
20686		{ 1, 0, -2, -2, -1 },
20687		{ 1, 0, 2, 2, 2 },
20688		{ 0, 1, 2, 0, 2 },
20689		{ 2, 0, -2, 0, 0 },
20690		{ 0, 0, 2, 2, 1 },
20691		{ 0, 1, -2, 0, -2 },
20692
20693		/* 41-50 */
20694		{ 0, 0, 0, 2, 1 },
20695		{ 1, 0, 2, -2, 1 },
20696		{ 2, 0, 0, -2, -1 },
20697		{ 2, 0, 2, -2, 2 },
20698		{ 2, 0, 2, 0, 1 },
20699		{ 0, 0, 0, 2, -1 },
20700		{ 0, 1, -2, 2, -1 },
20701		{ 1, 1, 0, -2, 0 },
20702		{ 2, 0, 0, -2, 1 },
20703		{ 1, 0, 0, 2, 0 },
20704
20705		/* 51-60 */
20706		{ 0, 1, 2, -2, 1 },
20707		{ 1, -1, 0, 0, 0 },
20708		{ 0, 1, -1, 1, -1 },
20709		{ 2, 0, -2, 0, -2 },
20710		{ 0, 1, 0, -2, 0 },
20711		{ 1, 0, 0, -1, 0 },
20712		{ 3, 0, 2, 0, 2 },
20713		{ 0, 0, 0, 1, 0 },
20714		{ 1, -1, 2, 0, 2 },
20715		{ 1, 1, -2, -2, -2 },
20716
20717		/* 61-70 */
20718		{ 1, 0, -2, 0, 0 },
20719		{ 2, 0, 0, 0, -1 },
20720		{ 0, 1, -2, -2, -2 },
20721		{ 1, 1, 2, 0, 2 },
20722		{ 2, 0, 0, 0, 1 },
20723		{ 1, 1, 0, 0, 0 },
20724		{ 1, 0, -2, 2, -1 },
20725		{ 1, 0, 2, 0, 0 },
20726		{ 1, -1, 0, -1, 0 },
20727		{ 1, 0, 0, 0, 2 },
20728
20729		/* 71-80 */
20730		{ 1, 0, -1, 0, -1 },
20731		{ 0, 0, 2, 1, 2 },
20732		{ 1, 0, -2, -4, -2 },
20733		{ 1, -1, 0, -1, -1 },
20734		{ 1, 0, 2, 2, 1 },
20735		{ 0, 2, -2, 2, -1 },
20736		{ 1, 0, 0, 0, -2 },
20737		{ 2, 0, -2, -2, -2 },
20738		{ 1, 1, 2, -2, 2 },
20739		{ 2, 0, -2, -4, -2 },
20740
20741		/* 81-90 */
20742		{ 1, 0, -4, 0, -2 },
20743		{ 2, 0, 2, -2, 1 },
20744		{ 1, 0, 0, -1, -1 },
20745		{ 2, 0, 2, 2, 2 },
20746		{ 3, 0, 0, 0, 0 },
20747		{ 1, 0, 0, 2, 1 },
20748		{ 0, 0, 2, -2, -1 },
20749		{ 3, 0, 2, -2, 2 },
20750		{ 0, 0, 4, -2, 2 },
20751		{ 1, 0, 0, -4, 0 },
20752
20753		/* 91-100 */
20754		{ 0, 1, 2, 0, 1 },
20755		{ 2, 0, 0, -4, 0 },
20756		{ 1, 1, 0, -2, -1 },
20757		{ 2, 0, -2, 0, 1 },
20758		{ 0, 0, 2, 0, -1 },
20759		{ 0, 1, -2, 0, -1 },
20760		{ 0, 1, 0, 0, 2 },
20761		{ 0, 0, 2, -1, 2 },
20762		{ 0, 0, 2, 4, 2 },
20763		{ 2, 1, 0, -2, 0 },
20764
20765		/* 101-110 */
20766		{ 1, 1, 0, -2, 1 },
20767		{ 1, -1, 0, -2, 0 },
20768		{ 1, -1, 0, -1, -2 },
20769		{ 1, -1, 0, 0, 1 },
20770		{ 0, 1, -2, 2, 0 },
20771		{ 0, 1, 0, 0, -2 },
20772		{ 1, -1, 2, 2, 2 },
20773		{ 1, 0, 0, 2, -1 },
20774		{ 1, -1, -2, -2, -2 },
20775		{ 3, 0, 2, 0, 1 },
20776
20777		/* 111-120 */
20778		{ 0, 1, 2, 2, 2 },
20779		{ 1, 0, 2, -2, 0 },
20780		{ 1, 1, -2, -2, -1 },
20781		{ 1, 0, 2, -4, 1 },
20782		{ 0, 1, -2, -2, -1 },
20783		{ 2, -1, 2, 0, 2 },
20784		{ 0, 0, 0, 2, 2 },
20785		{ 1, -1, 2, 0, 1 },
20786		{ 1, -1, -2, 0, -2 },
20787		{ 0, 1, 0, 2, 0 },
20788
20789		/* 121-130 */
20790		{ 0, 1, 2, -2, 0 },
20791		{ 0, 0, 0, 1, 1 },
20792		{ 1, 0, -2, -2, 0 },
20793		{ 0, 3, 2, -2, 2 },
20794		{ 2, 1, 2, 0, 2 },
20795		{ 1, 1, 0, 0, 1 },
20796		{ 2, 0, 0, 2, 0 },
20797		{ 1, 1, 2, 0, 1 },
20798		{ 1, 0, 0, -2, -2 },
20799		{ 1, 0, -2, 2, 0 },
20800
20801		/* 131-140 */
20802		{ 1, 0, -1, 0, -2 },
20803		{ 0, 1, 0, -2, 1 },
20804		{ 0, 1, 0, 1, 0 },
20805		{ 0, 0, 0, 1, -1 },
20806		{ 1, 0, -2, 2, -2 },
20807		{ 1, -1, 0, 0, -1 },
20808		{ 0, 0, 0, 4, 0 },
20809		{ 1, -1, 0, 2, 0 },
20810		{ 1, 0, 2, 1, 2 },
20811		{ 1, 0, 2, -1, 2 },
20812
20813		/* 141-150 */
20814		{ 0, 0, 2, 1, 1 },
20815		{ 1, 0, 0, -2, 2 },
20816		{ 1, 0, -2, 0, 1 },
20817		{ 1, 0, -2, -4, -1 },
20818		{ 0, 0, 2, 2, 0 },
20819		{ 1, 1, 2, -2, 1 },
20820		{ 1, 0, -2, 1, -1 },
20821		{ 0, 0, 1, 0, 1 },
20822		{ 2, 0, -2, -2, -1 },
20823		{ 4, 0, 2, 0, 2 },
20824
20825		/* 151-160 */
20826		{ 2, -1, 0, 0, 0 },
20827		{ 2, 1, 2, -2, 2 },
20828		{ 0, 1, 2, 1, 2 },
20829		{ 1, 0, 4, -2, 2 },
20830		{ 1, 1, 0, 0, -1 },
20831		{ 2, 0, 2, 0, 0 },
20832		{ 2, 0, -2, -4, -1 },
20833		{ 1, 0, -1, 0, 0 },
20834		{ 1, 0, 0, 1, 0 },
20835		{ 0, 1, 0, 2, 1 },
20836
20837		/* 161-170 */
20838		{ 1, 0, -4, 0, -1 },
20839		{ 1, 0, 0, -4, -1 },
20840		{ 2, 0, 2, 2, 1 },
20841		{ 2, 1, 0, 0, 0 },
20842		{ 0, 0, 2, -3, 2 },
20843		{ 1, 2, 0, -2, 0 },
20844		{ 0, 3, 0, 0, 0 },
20845		{ 0, 0, 4, 0, 2 },
20846		{ 0, 0, 2, -4, 1 },
20847		{ 2, 0, 0, -2, -2 },
20848
20849		/* 171-180 */
20850		{ 1, 1, -2, -4, -2 },
20851		{ 0, 1, 0, -2, -1 },
20852		{ 0, 0, 0, 4, 1 },
20853		{ 3, 0, 2, -2, 1 },
20854		{ 1, 0, 2, 4, 2 },
20855		{ 1, 1, -2, 0, -2 },
20856		{ 0, 0, 4, -2, 1 },
20857		{ 2, -2, 0, -2, 0 },
20858		{ 2, 1, 0, -2, -1 },
20859		{ 0, 2, 0, -2, 0 },
20860
20861		/* 181-190 */
20862		{ 1, 0, 0, -1, 1 },
20863		{ 1, 1, 2, 2, 2 },
20864		{ 3, 0, 0, 0, -1 },
20865		{ 2, 0, 0, -4, -1 },
20866		{ 3, 0, 2, 2, 2 },
20867		{ 0, 0, 2, 4, 1 },
20868		{ 0, 2, -2, -2, -2 },
20869		{ 1, -1, 0, -2, -1 },
20870		{ 0, 0, 2, -1, 1 },
20871		{ 2, 0, 0, 2, 1 },
20872
20873		/* 191-200 */
20874		{ 1, -1, -2, 2, -1 },
20875		{ 0, 0, 0, 2, -2 },
20876		{ 2, 0, 0, -4, 1 },
20877		{ 1, 0, 0, -4, 1 },
20878		{ 2, 0, 2, -4, 1 },
20879		{ 4, 0, 2, -2, 2 },
20880		{ 2, 1, -2, 0, -1 },
20881		{ 2, 1, -2, -4, -2 },
20882		{ 3, 0, 0, -4, 0 },
20883		{ 1, -1, 2, 2, 1 },
20884
20885		/* 201-210 */
20886		{ 1, -1, -2, 0, -1 },
20887		{ 0, 2, 0, 0, 1 },
20888		{ 1, 2, -2, -2, -2 },
20889		{ 1, 1, 0, -4, 0 },
20890		{ 2, 0, 0, -2, 2 },
20891		{ 0, 2, 2, -2, 1 },
20892		{ 1, 0, 2, 0, -1 },
20893		{ 2, 1, 0, -2, 1 },
20894		{ 2, -1, -2, 0, -1 },
20895		{ 1, -1, -2, -2, -1 },
20896
20897		/* 211-220 */
20898		{ 0, 1, -2, 1, -2 },
20899		{ 1, 0, -4, 2, -2 },
20900		{ 0, 1, 2, 2, 1 },
20901		{ 3, 0, 0, 0, 1 },
20902		{ 2, -1, 2, 2, 2 },
20903		{ 0, 1, -2, -4, -2 },
20904		{ 1, 0, -2, -3, -2 },
20905		{ 2, 0, 0, 0, 2 },
20906		{ 1, -1, 0, -2, -2 },
20907		{ 2, 0, -2, 2, -1 },
20908
20909		/* 221-230 */
20910		{ 0, 2, -2, 0, -2 },
20911		{ 3, 0, -2, 0, -1 },
20912		{ 2, -1, 2, 0, 1 },
20913		{ 1, 0, -2, -1, -2 },
20914		{ 0, 0, 2, 0, 3 },
20915		{ 2, 0, -4, 0, -2 },
20916		{ 2, 1, 0, -4, 0 },
20917		{ 1, 1, -2, 1, -1 },
20918		{ 0, 2, 2, 0, 2 },
20919		{ 1, -1, 2, -2, 2 },
20920
20921		/* 231-240 */
20922		{ 1, -1, 0, -2, 1 },
20923		{ 2, 1, 2, 0, 1 },
20924		{ 1, 0, 2, -4, 2 },
20925		{ 1, 1, -2, 0, -1 },
20926		{ 1, 1, 0, 2, 0 },
20927		{ 1, 0, 0, -3, 0 },
20928		{ 2, 0, 2, -1, 2 },
20929		{ 0, 2, 0, 0, -1 },
20930		{ 2, -1, 0, -2, 0 },
20931		{ 4, 0, 0, 0, 0 },
20932
20933		/* 241-250 */
20934		{ 2, 1, -2, -2, -2 },
20935		{ 0, 2, -2, 2, 0 },
20936		{ 1, 0, 2, 1, 1 },
20937		{ 1, 0, -1, 0, -3 },
20938		{ 3, -1, 2, 0, 2 },
20939		{ 2, 0, 2, -2, 0 },
20940		{ 1, -2, 0, 0, 0 },
20941		{ 2, 0, 0, 0, -2 },
20942		{ 1, 0, 0, 4, 0 },
20943		{ 0, 1, 0, 1, 1 },
20944
20945		/* 251-260 */
20946		{ 1, 0, 2, 2, 0 },
20947		{ 0, 1, 0, 2, -1 },
20948		{ 0, 1, 0, 1, -1 },
20949		{ 0, 0, 2, -2, 3 },
20950		{ 3, 1, 2, 0, 2 },
20951		{ 1, 1, 2, 1, 2 },
20952		{ 1, 1, -2, 2, -1 },
20953		{ 2, -1, 2, -2, 2 },
20954		{ 1, -2, 2, 0, 2 },
20955		{ 1, 0, 2, -4, 0 },
20956
20957		/* 261-270 */
20958		{ 0, 0, 1, 0, 0 },
20959		{ 1, 0, 2, -3, 1 },
20960		{ 1, -2, 0, -2, 0 },
20961		{ 2, 0, 0, 2, -1 },
20962		{ 1, 1, 2, -4, 1 },
20963		{ 4, 0, 2, 0, 1 },
20964		{ 0, 1, 2, 1, 1 },
20965		{ 1, 2, 2, -2, 2 },
20966		{ 2, 0, 2, 1, 2 },
20967		{ 2, 1, 2, -2, 1 },
20968
20969		/* 271-280 */
20970		{ 1, 0, 2, -1, 1 },
20971		{ 1, 0, 4, -2, 1 },
20972		{ 1, -1, 2, -2, 1 },
20973		{ 0, 1, 0, -4, 0 },
20974		{ 3, 0, -2, -2, -2 },
20975		{ 0, 0, 4, -4, 2 },
20976		{ 2, 0, -4, -2, -2 },
20977		{ 2, -2, 0, -2, -1 },
20978		{ 1, 0, 2, -2, -1 },
20979		{ 2, 0, -2, -6, -2 },
20980
20981		/* 281-290 */
20982		{ 1, 0, -2, 1, -2 },
20983		{ 1, 0, -2, 2, 1 },
20984		{ 1, -1, 0, 2, -1 },
20985		{ 1, 0, -2, 1, 0 },
20986		{ 2, -1, 0, -2, 1 },
20987		{ 1, -1, 0, 2, 1 },
20988		{ 2, 0, -2, -2, 0 },
20989		{ 1, 0, 2, -3, 2 },
20990		{ 0, 0, 0, 4, -1 },
20991		{ 2, -1, 0, 0, 1 },
20992
20993		/* 291-300 */
20994		{ 2, 0, 4, -2, 2 },
20995		{ 0, 0, 2, 3, 2 },
20996		{ 0, 1, 4, -2, 2 },
20997		{ 0, 1, -2, 2, 1 },
20998		{ 1, 1, 0, 2, 1 },
20999		{ 1, 0, 0, 4, 1 },
21000		{ 0, 0, 4, 0, 1 },
21001		{ 2, 0, 0, -3, 0 },
21002		{ 1, 0, 0, -1, -2 },
21003		{ 1, -2, -2, -2, -2 },
21004
21005		/* 301-310 */
21006		{ 3, 0, 0, 2, 0 },
21007		{ 2, 0, 2, -4, 2 },
21008		{ 1, 1, -2, -4, -1 },
21009		{ 1, 0, -2, -6, -2 },
21010		{ 2, -1, 0, 0, -1 },
21011		{ 2, -1, 0, 2, 0 },
21012		{ 0, 1, 2, -2, -1 },
21013		{ 1, 1, 0, 1, 0 },
21014		{ 1, 2, 0, -2, -1 },
21015		{ 1, 0, 0, 1, -1 },
21016
21017		/* 311-320 */
21018		{ 0, 0, 1, 0, 2 },
21019		{ 3, 1, 2, -2, 2 },
21020		{ 1, 0, -4, -2, -2 },
21021		{ 1, 0, 2, 4, 1 },
21022		{ 1, -2, 2, 2, 2 },
21023		{ 1, -1, -2, -4, -2 },
21024		{ 0, 0, 2, -4, 2 },
21025		{ 0, 0, 2, -3, 1 },
21026		{ 2, 1, -2, 0, 0 },
21027		{ 3, 0, -2, -2, -1 },
21028
21029		/* 321-330 */
21030		{ 2, 0, 2, 4, 2 },
21031		{ 0, 0, 0, 0, 3 },
21032		{ 2, -1, -2, -2, -2 },
21033		{ 2, 0, 0, -1, 0 },
21034		{ 3, 0, 2, -4, 2 },
21035		{ 2, 1, 2, 2, 2 },
21036		{ 0, 0, 3, 0, 3 },
21037		{ 1, 1, 2, 2, 1 },
21038		{ 2, 1, 0, 0, -1 },
21039		{ 1, 2, 0, -2, 1 },
21040
21041		/* 331-340 */
21042		{ 3, 0, 2, 2, 1 },
21043		{ 1, -1, -2, 2, -2 },
21044		{ 1, 1, 0, -1, 0 },
21045		{ 1, 2, 0, 0, 0 },
21046		{ 1, 0, 4, 0, 2 },
21047		{ 1, -1, 2, 4, 2 },
21048		{ 2, 1, 0, 0, 1 },
21049		{ 1, 0, 0, 2, 2 },
21050		{ 1, -1, -2, 2, 0 },
21051		{ 0, 2, -2, -2, -1 },
21052
21053		/* 341-350 */
21054		{ 2, 0, -2, 0, 2 },
21055		{ 5, 0, 2, 0, 2 },
21056		{ 3, 0, -2, -6, -2 },
21057		{ 1, -1, 2, -1, 2 },
21058		{ 3, 0, 0, -4, -1 },
21059		{ 1, 0, 0, 1, 1 },
21060		{ 1, 0, -4, 2, -1 },
21061		{ 0, 1, 2, -4, 1 },
21062		{ 1, 2, 2, 0, 2 },
21063		{ 0, 1, 0, -2, -2 },
21064
21065		/* 351-360 */
21066		{ 0, 0, 2, -1, 0 },
21067		{ 1, 0, 1, 0, 1 },
21068		{ 0, 2, 0, -2, 1 },
21069		{ 3, 0, 2, 0, 0 },
21070		{ 1, 1, -2, 1, 0 },
21071		{ 2, 1, -2, -4, -1 },
21072		{ 3, -1, 0, 0, 0 },
21073		{ 2, -1, -2, 0, 0 },
21074		{ 4, 0, 2, -2, 1 },
21075		{ 2, 0, -2, 2, 0 },
21076
21077		/* 361-370 */
21078		{ 1, 1, 2, -2, 0 },
21079		{ 1, 0, -2, 4, -1 },
21080		{ 1, 0, -2, -2, 1 },
21081		{ 2, 0, 2, -4, 0 },
21082		{ 1, 1, 0, -2, -2 },
21083		{ 1, 1, -2, -2, 0 },
21084		{ 1, 0, 1, -2, 1 },
21085		{ 2, -1, -2, -4, -2 },
21086		{ 3, 0, -2, 0, -2 },
21087		{ 0, 1, -2, -2, 0 },
21088
21089		/* 371-380 */
21090		{ 3, 0, 0, -2, -1 },
21091		{ 1, 0, -2, -3, -1 },
21092		{ 0, 1, 0, -4, -1 },
21093		{ 1, -2, 2, -2, 1 },
21094		{ 0, 1, -2, 1, -1 },
21095		{ 1, -1, 0, 0, 2 },
21096		{ 2, 0, 0, 1, 0 },
21097		{ 1, -2, 0, 2, 0 },
21098		{ 1, 2, -2, -2, -1 },
21099		{ 0, 0, 4, -4, 1 },
21100
21101		/* 381-390 */
21102		{ 0, 1, 2, 4, 2 },
21103		{ 0, 1, -4, 2, -2 },
21104		{ 3, 0, -2, 0, 0 },
21105		{ 2, -1, 2, 2, 1 },
21106		{ 0, 1, -2, -4, -1 },
21107		{ 4, 0, 2, 2, 2 },
21108		{ 2, 0, -2, -3, -2 },
21109		{ 2, 0, 0, -6, 0 },
21110		{ 1, 0, 2, 0, 3 },
21111		{ 3, 1, 0, 0, 0 },
21112
21113		/* 391-400 */
21114		{ 3, 0, 0, -4, 1 },
21115		{ 1, -1, 2, 0, 0 },
21116		{ 1, -1, 0, -4, 0 },
21117		{ 2, 0, -2, 2, -2 },
21118		{ 1, 1, 0, -2, 2 },
21119		{ 4, 0, 0, -2, 0 },
21120		{ 2, 2, 0, -2, 0 },
21121		{ 0, 1, 2, 0, 0 },
21122		{ 1, 1, 0, -4, 1 },
21123		{ 1, 0, 0, -4, -2 },
21124
21125		/* 401-410 */
21126		{ 0, 0, 0, 1, 2 },
21127		{ 3, 0, 0, 2, 1 },
21128		{ 1, 1, 0, -4, -1 },
21129		{ 0, 0, 2, 2, -1 },
21130		{ 1, 1, 2, 0, 0 },
21131		{ 1, -1, 2, -4, 1 },
21132		{ 1, 1, 0, 0, 2 },
21133		{ 0, 0, 2, 6, 2 },
21134		{ 4, 0, -2, -2, -1 },
21135		{ 2, 1, 0, -4, -1 },
21136
21137		/* 411-420 */
21138		{ 0, 0, 0, 3, 1 },
21139		{ 1, -1, -2, 0, 0 },
21140		{ 0, 0, 2, 1, 0 },
21141		{ 1, 0, 0, 2, -2 },
21142		{ 3, -1, 2, 2, 2 },
21143		{ 3, -1, 2, -2, 2 },
21144		{ 1, 0, 0, -1, 2 },
21145		{ 1, -2, 2, -2, 2 },
21146		{ 0, 1, 0, 2, 2 },
21147		{ 0, 1, -2, -1, -2 },
21148
21149		/* 421-430 */
21150		{ 1, 1, -2, 0, 0 },
21151		{ 0, 2, 2, -2, 0 },
21152		{ 3, -1, -2, -1, -2 },
21153		{ 1, 0, 0, -6, 0 },
21154		{ 1, 0, -2, -4, 0 },
21155		{ 2, 1, 0, -4, 1 },
21156		{ 2, 0, 2, 0, -1 },
21157		{ 2, 0, -4, 0, -1 },
21158		{ 0, 0, 3, 0, 2 },
21159		{ 2, 1, -2, -2, -1 },
21160
21161		/* 431-440 */
21162		{ 1, -2, 0, 0, 1 },
21163		{ 2, -1, 0, -4, 0 },
21164		{ 0, 0, 0, 3, 0 },
21165		{ 5, 0, 2, -2, 2 },
21166		{ 1, 2, -2, -4, -2 },
21167		{ 1, 0, 4, -4, 2 },
21168		{ 0, 0, 4, -1, 2 },
21169		{ 3, 1, 0, -4, 0 },
21170		{ 3, 0, 0, -6, 0 },
21171		{ 2, 0, 0, 2, 2 },
21172
21173		/* 441-450 */
21174		{ 2, -2, 2, 0, 2 },
21175		{ 1, 0, 0, -3, 1 },
21176		{ 1, -2, -2, 0, -2 },
21177		{ 1, -1, -2, -3, -2 },
21178		{ 0, 0, 2, -2, -2 },
21179		{ 2, 0, -2, -4, 0 },
21180		{ 1, 0, -4, 0, 0 },
21181		{ 0, 1, 0, -1, 0 },
21182		{ 4, 0, 0, 0, -1 },
21183		{ 3, 0, 2, -1, 2 },
21184
21185		/* 451-460 */
21186		{ 3, -1, 2, 0, 1 },
21187		{ 2, 0, 2, -1, 1 },
21188		{ 1, 2, 2, -2, 1 },
21189		{ 1, 1, 0, 2, -1 },
21190		{ 0, 2, 2, 0, 1 },
21191		{ 3, 1, 2, 0, 1 },
21192		{ 1, 1, 2, 1, 1 },
21193		{ 1, 1, 0, -1, 1 },
21194		{ 1, -2, 0, -2, -1 },
21195		{ 4, 0, 0, -4, 0 },
21196
21197		/* 461-470 */
21198		{ 2, 1, 0, 2, 0 },
21199		{ 1, -1, 0, 4, 0 },
21200		{ 0, 1, 0, -2, 2 },
21201		{ 0, 0, 2, 0, -2 },
21202		{ 1, 0, -1, 0, 1 },
21203		{ 3, 0, 2, -2, 0 },
21204		{ 2, 0, 2, 2, 0 },
21205		{ 1, 2, 0, -4, 0 },
21206		{ 1, -1, 0, -3, 0 },
21207		{ 0, 1, 0, 4, 0 },
21208
21209		/* 471 - 480 */
21210		{ 0, 1, -2, 0, 0 },
21211		{ 2, 2, 2, -2, 2 },
21212		{ 0, 0, 0, 1, -2 },
21213		{ 0, 2, -2, 0, -1 },
21214		{ 4, 0, 2, -4, 2 },
21215		{ 2, 0, -4, 2, -2 },
21216		{ 2, -1, -2, 0, -2 },
21217		{ 1, 1, 4, -2, 2 },
21218		{ 1, 1, 2, -4, 2 },
21219		{ 1, 0, 2, 3, 2 },
21220
21221		/* 481-490 */
21222		{ 1, 0, 0, 4, -1 },
21223		{ 0, 0, 0, 4, 2 },
21224		{ 2, 0, 0, 4, 0 },
21225		{ 1, 1, -2, 2, 0 },
21226		{ 2, 1, 2, 1, 2 },
21227		{ 2, 1, 2, -4, 1 },
21228		{ 2, 0, 2, 1, 1 },
21229		{ 2, 0, -4, -2, -1 },
21230		{ 2, 0, -2, -6, -1 },
21231		{ 2, -1, 2, -1, 2 },
21232
21233		/* 491-500 */
21234		{ 1, -2, 2, 0, 1 },
21235		{ 1, -2, 0, -2, 1 },
21236		{ 1, -1, 0, -4, -1 },
21237		{ 0, 2, 2, 2, 2 },
21238		{ 0, 2, -2, -4, -2 },
21239		{ 0, 1, 2, 3, 2 },
21240		{ 0, 1, 0, -4, 1 },
21241		{ 3, 0, 0, -2, 1 },
21242		{ 2, 1, -2, 0, 1 },
21243		{ 2, 0, 4, -2, 1 },
21244
21245		/* 501-510 */
21246		{ 2, 0, 0, -3, -1 },
21247		{ 2, -2, 0, -2, 1 },
21248		{ 2, -1, 2, -2, 1 },
21249		{ 1, 0, 0, -6, -1 },
21250		{ 1, -2, 0, 0, -1 },
21251		{ 1, -2, -2, -2, -1 },
21252		{ 0, 1, 4, -2, 1 },
21253		{ 0, 0, 2, 3, 1 },
21254		{ 2, -1, 0, -1, 0 },
21255		{ 1, 3, 0, -2, 0 },
21256
21257		/* 511-520 */
21258		{ 0, 3, 0, -2, 0 },
21259		{ 2, -2, 2, -2, 2 },
21260		{ 0, 0, 4, -2, 0 },
21261		{ 4, -1, 2, 0, 2 },
21262		{ 2, 2, -2, -4, -2 },
21263		{ 4, 1, 2, 0, 2 },
21264		{ 4, -1, -2, -2, -2 },
21265		{ 2, 1, 0, -2, -2 },
21266		{ 2, 1, -2, -6, -2 },
21267		{ 2, 0, 0, -1, 1 },
21268
21269		/* 521-530 */
21270		{ 2, -1, -2, 2, -1 },
21271		{ 1, 1, -2, 2, -2 },
21272		{ 1, 1, -2, -3, -2 },
21273		{ 1, 0, 3, 0, 3 },
21274		{ 1, 0, -2, 1, 1 },
21275		{ 1, 0, -2, 0, 2 },
21276		{ 1, -1, 2, 1, 2 },
21277		{ 1, -1, 0, 0, -2 },
21278		{ 1, -1, -4, 2, -2 },
21279		{ 0, 3, -2, -2, -2 },
21280
21281		/* 531-540 */
21282		{ 0, 1, 0, 4, 1 },
21283		{ 0, 0, 4, 2, 2 },
21284		{ 3, 0, -2, -2, 0 },
21285		{ 2, -2, 0, 0, 0 },
21286		{ 1, 1, 2, -4, 0 },
21287		{ 1, 1, 0, -3, 0 },
21288		{ 1, 0, 2, -3, 0 },
21289		{ 1, -1, 2, -2, 0 },
21290		{ 0, 2, 0, 2, 0 },
21291		{ 0, 0, 2, 4, 0 },
21292
21293		/* 541-550 */
21294		{ 1, 0, 1, 0, 0 },
21295		{ 3, 1, 2, -2, 1 },
21296		{ 3, 0, 4, -2, 2 },
21297		{ 3, 0, 2, 1, 2 },
21298		{ 3, 0, 0, 2, -1 },
21299		{ 3, 0, 0, 0, 2 },
21300		{ 3, 0, -2, 2, -1 },
21301		{ 2, 0, 4, -4, 2 },
21302		{ 2, 0, 2, -3, 2 },
21303		{ 2, 0, 0, 4, 1 },
21304
21305		/* 551-560 */
21306		{ 2, 0, 0, -3, 1 },
21307		{ 2, 0, -4, 2, -1 },
21308		{ 2, 0, -2, -2, 1 },
21309		{ 2, -2, 2, 2, 2 },
21310		{ 2, -2, 0, -2, -2 },
21311		{ 2, -1, 0, 2, 1 },
21312		{ 2, -1, 0, 2, -1 },
21313		{ 1, 1, 2, 4, 2 },
21314		{ 1, 1, 0, 1, 1 },
21315		{ 1, 1, 0, 1, -1 },
21316
21317		/* 561-570 */
21318		{ 1, 1, -2, -6, -2 },
21319		{ 1, 0, 0, -3, -1 },
21320		{ 1, 0, -4, -2, -1 },
21321		{ 1, 0, -2, -6, -1 },
21322		{ 1, -2, 2, 2, 1 },
21323		{ 1, -2, -2, 2, -1 },
21324		{ 1, -1, -2, -4, -1 },
21325		{ 0, 2, 0, 0, 2 },
21326		{ 0, 1, 2, -4, 2 },
21327		{ 0, 1, -2, 4, -1 },
21328
21329		/* 571-580 */
21330		{ 5, 0, 0, 0, 0 },
21331		{ 3, 0, 0, -3, 0 },
21332		{ 2, 2, 0, -4, 0 },
21333		{ 1, -1, 2, 2, 0 },
21334		{ 0, 1, 0, 3, 0 },
21335		{ 4, 0, -2, 0, -1 },
21336		{ 3, 0, -2, -6, -1 },
21337		{ 3, 0, -2, -1, -1 },
21338		{ 2, 1, 2, 2, 1 },
21339		{ 2, 1, 0, 2, 1 },
21340
21341		/* 581-590 */
21342		{ 2, 0, 2, 4, 1 },
21343		{ 2, 0, 2, -6, 1 },
21344		{ 2, 0, 2, -2, -1 },
21345		{ 2, 0, 0, -6, -1 },
21346		{ 2, -1, -2, -2, -1 },
21347		{ 1, 2, 2, 0, 1 },
21348		{ 1, 2, 0, 0, 1 },
21349		{ 1, 0, 4, 0, 1 },
21350		{ 1, 0, 2, -6, 1 },
21351		{ 1, 0, 2, -4, -1 },
21352
21353		/* 591-600 */
21354		{ 1, 0, -1, -2, -1 },
21355		{ 1, -1, 2, 4, 1 },
21356		{ 1, -1, 2, -3, 1 },
21357		{ 1, -1, 0, 4, 1 },
21358		{ 1, -1, -2, 1, -1 },
21359		{ 0, 1, 2, -2, 3 },
21360		{ 3, 0, 0, -2, 0 },
21361		{ 1, 0, 1, -2, 0 },
21362		{ 0, 2, 0, -4, 0 },
21363		{ 0, 0, 2, -4, 0 },
21364
21365		/* 601-610 */
21366		{ 0, 0, 1, -1, 0 },
21367		{ 0, 0, 0, 6, 0 },
21368		{ 0, 2, 0, 0, -2 },
21369		{ 0, 1, -2, 2, -3 },
21370		{ 4, 0, 0, 2, 0 },
21371		{ 3, 0, 0, -1, 0 },
21372		{ 3, -1, 0, 2, 0 },
21373		{ 2, 1, 0, 1, 0 },
21374		{ 2, 1, 0, -6, 0 },
21375		{ 2, -1, 2, 0, 0 },
21376
21377		/* 611-620 */
21378		{ 1, 0, 2, -1, 0 },
21379		{ 1, -1, 0, 1, 0 },
21380		{ 1, -1, -2, -2, 0 },
21381		{ 0, 1, 2, 2, 0 },
21382		{ 0, 0, 2, -3, 0 },
21383		{ 2, 2, 0, -2, -1 },
21384		{ 2, -1, -2, 0, 1 },
21385		{ 1, 2, 2, -4, 1 },
21386		{ 0, 1, 4, -4, 2 },
21387		{ 0, 0, 0, 3, 2 },
21388
21389		/* 621-630 */
21390		{ 5, 0, 2, 0, 1 },
21391		{ 4, 1, 2, -2, 2 },
21392		{ 4, 0, -2, -2, 0 },
21393		{ 3, 1, 2, 2, 2 },
21394		{ 3, 1, 0, -2, 0 },
21395		{ 3, 1, -2, -6, -2 },
21396		{ 3, 0, 0, 0, -2 },
21397		{ 3, 0, -2, -4, -2 },
21398		{ 3, -1, 0, -3, 0 },
21399		{ 3, -1, 0, -2, 0 },
21400
21401		/* 631-640 */
21402		{ 2, 1, 2, 0, 0 },
21403		{ 2, 1, 2, -4, 2 },
21404		{ 2, 1, 2, -2, 0 },
21405		{ 2, 1, 0, -3, 0 },
21406		{ 2, 1, -2, 0, -2 },
21407		{ 2, 0, 0, -4, 2 },
21408		{ 2, 0, 0, -4, -2 },
21409		{ 2, 0, -2, -5, -2 },
21410		{ 2, -1, 2, 4, 2 },
21411		{ 2, -1, 0, -2, 2 },
21412
21413		/* 641-650 */
21414		{ 1, 3, -2, -2, -2 },
21415		{ 1, 1, 0, 0, -2 },
21416		{ 1, 1, 0, -6, 0 },
21417		{ 1, 1, -2, 1, -2 },
21418		{ 1, 1, -2, -1, -2 },
21419		{ 1, 0, 2, 1, 0 },
21420		{ 1, 0, 0, 3, 0 },
21421		{ 1, 0, 0, -4, 2 },
21422		{ 1, 0, -2, 4, -2 },
21423		{ 1, -2, 0, -1, 0 },
21424
21425		/* 651-NFLS */
21426		{ 0, 1, -4, 2, -1 },
21427		{ 1, 0, -2, 0, -3 },
21428		{ 0, 0, 4, -4, 4 }
21429		};
21430	2	}
21431
21432
21433		/* Fundamental-argument multipliers: planetary terms */
21434	2	private static final int mfapl[][] = {
21435
21436		/* 1-10 */
21437		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 5, 0, 0, 0 },
21438		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -1 },
21439		{ 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -2 },
21440		{ 0, 0, 1, -1, 1, 0, -8, 12, 0, 0, 0, 0, 0, 0 },
21441		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2 },
21442		{ 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21443		{ 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
21444		{ 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 0 },
21445		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21446		{ 0, 0, 0, 0, 1, 0, 0, -1, 2, 0, 0, 0, 0, 0 },
21447
21448		/* 11-20 */
21449		{ 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, -1 },
21450		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 2, -5, 0, 0, 0 },
21451		{ 0, 0, 2, -2, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21452		{ 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -2 },
21453		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, -1, 0, 0, 0, 2 },
21454		{ 0, 0, 0, 0, 0, 0, 0, 2, -8, 3, 0, 0, 0, -2 },
21455		{ 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -2 },
21456		{ 0, 0, 0, 0, 0, 0, 0, 6, -8, 3, 0, 0, 0, 2 },
21457		{ 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0 },
21458		{ 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 0 },
21459
21460		/* 21-30 */
21461		{ 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
21462		{ 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2 },
21463		{ 0, 0, 0, 0, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21464		{ 0, 0, 0, 0, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21465		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0 },
21466		{ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2 },
21467		{ 0, 0, 1, -1, 1, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21468		{ 2, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21469		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1 },
21470		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21471
21472		/* 31-40 */
21473		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
21474		{ 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 0 },
21475		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2 },
21476		{ 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -2 },
21477		{ 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0 },
21478		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 1 },
21479		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21480		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21481		{ 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 0 },
21482		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -1, 0, 0, 0 },
21483
21484		/* 41-50 */
21485		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0 },
21486		{ 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -2 },
21487		{ 0, 0, 1, -1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21488		{ 0, 0, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 2 },
21489		{ 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, -2 },
21490		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 },
21491		{ 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 2 },
21492		{ 1, 0, 0, 0, 0, 0,-18, 16, 0, 0, 0, 0, 0, 0 },
21493		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21494		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2 },
21495
21496		/* 51-60 */
21497		{ 0, 0, 1, -1, 1, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
21498		{ 1, 0, 0, 0, 0, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
21499		{ 0, 0, 2, -2, 0, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21500		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 2 },
21501		{ 1, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21502		{ 0, 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 2 },
21503		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1 },
21504		{ 1, 0, -2, 0, -2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21505		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 2, 0, 0, 0 },
21506		{ 0, 0, 2, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21507
21508		/* 61-70 */
21509		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2 },
21510		{ 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, -2 },
21511		{ 0, 0, 1, -1, 1, 0, 0, 3, -8, 3, 0, 0, 0, 0 },
21512		{ 0, 0, 0, 0, 0, 0, 8,-11, 0, 0, 0, 0, 0, -2 },
21513		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2 },
21514		{ 0, 0, 0, 0, 0, 0, 0, 8,-16, 4, 5, 0, 0, 2 },
21515		{ 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -1 },
21516		{ 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, -1 },
21517		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -2 },
21518		{ 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0 },
21519
21520		/* 71-80 */
21521		{ 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -2 },
21522		{ 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0, 2 },
21523		{ 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0, -2 },
21524		{ 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -2 },
21525		{ 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -2 },
21526		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 2 },
21527		{ 0, 0, 1, -1, 1, 0, 0, -5, 8, -3, 0, 0, 0, 0 },
21528		{ 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2 },
21529		{ 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 2 },
21530		{ 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 0 },
21531
21532		/* 81-90 */
21533		{ 2, 0, 0, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21534		{ 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, -1 },
21535		{ 2, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21536		{ 0, 0, 0, 0, 1, 0, 8,-13, 0, 0, 0, 0, 0, 0 },
21537		{ 0, 0, 0, 0, 1, 0, 0, 0, 0, -2, 5, 0, 0, 0 },
21538		{ 1, 0, 0, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21539		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2 },
21540		{ 1, 0, 0, 0, -1, 0,-18, 16, 0, 0, 0, 0, 0, 0 },
21541		{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, -5, 0, 0, 0 },
21542		{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0 },
21543
21544		/* 91-100 */
21545		{ 1, 0, 0, -2, 0, 0, 19,-21, 3, 0, 0, 0, 0, 0 },
21546		{ 0, 0, 0, 0, 1, 0, -8, 13, 0, 0, 0, 0, 0, 0 },
21547		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 1, 0, 0, 0 },
21548		{ 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -2 },
21549		{ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2 },
21550		{ 1, 0, 0, 0, 1, 0,-18, 16, 0, 0, 0, 0, 0, 0 },
21551		{ 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, -1 },
21552		{ 0, 0, 0, 0, 0, 0, 0, 6,-16, 4, 5, 0, 0, -2 },
21553		{ 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -2 },
21554		{ 0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0, -2 },
21555
21556		/* 101-110 */
21557		{ 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, -1 },
21558		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1 },
21559		{ 2, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21560		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1 },
21561		{ 0, 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0 },
21562		{ 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0 },
21563		{ 2, 0, 0, -2, -1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21564		{ 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 0 },
21565		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0 },
21566		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2 },
21567
21568		/* 111-120 */
21569		{ 0, 0, 0, 0, 1, 0, 0, 1, -2, 0, 0, 0, 0, 0 },
21570		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2 },
21571		{ 0, 0, 2, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21572		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -3, 0, 0, 0, 0 },
21573		{ 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, -1 },
21574		{ 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 2 },
21575		{ 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 0 },
21576		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21577		{ 2, 0, 0, -2, 0, 0, -6, 8, 0, 0, 0, 0, 0, 0 },
21578		{ 0, 0, 1, -1, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
21579
21580		/* 121-130 */
21581		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1 },
21582		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21583		{ 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, -1 },
21584		{ 0, 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0 },
21585		{ 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -2 },
21586		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0 },
21587		{ 0, 0, 0, 0, 0, 0, 8,-10, 0, 0, 0, 0, 0, -2 },
21588		{ 0, 0, 1, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21589		{ 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -2 },
21590		{ 1, 0, 0, -1, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21591
21592		/* 131-140 */
21593		{ 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, -1 },
21594		{ 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 0 },
21595		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1 },
21596		{ 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, -1 },
21597		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 },
21598		{ 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 2 },
21599		{ 0, 0, 0, 0, 0, 0, 0, 4, 0, -3, 0, 0, 0, 2 },
21600		{ 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 1 },
21601		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1 },
21602		{ 0, 0, 0, 0, 1, 0, 2, -3, 0, 0, 0, 0, 0, 0 },
21603
21604		/* 141-150 */
21605		{ 1, 0, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21606		{ 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, -1 },
21607		{ 0, 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 2 },
21608		{ 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 2 },
21609		{ 0, 0, 0, 0, 0, 0, 9,-11, 0, 0, 0, 0, 0, -2 },
21610		{ 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -1 },
21611		{ 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0 },
21612		{ 0, 0, 1, -1, 1, 0, -4, 5, 0, 0, 0, 0, 0, 0 },
21613		{ 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0, 0 },
21614		{ 0, 0, 0, 0, 0, 0, 0, 4, 0, -1, 0, 0, 0, 2 },
21615
21616		/* 151-160 */
21617		{ 1, 0, 0, -1, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21618		{ 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21619		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, -4, 10, 0, 0, 0 },
21620		{ 0, 0, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
21621		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0 },
21622		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0 },
21623		{ 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 2 },
21624		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, -2 },
21625		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, -2 },
21626		{ 0, 0, 2, -2, 1, 0, -4, 4, 0, 0, 0, 0, 0, 0 },
21627
21628		/* 161-170 */
21629		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -1, 0, 0, 2 },
21630		{ 0, 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 2 },
21631		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0 },
21632		{ 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, -1 },
21633		{ 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, -1 },
21634		{ 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0, 0 },
21635		{ 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 1 },
21636		{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0 },
21637		{ 0, 0, 2, -2, 1, 0, 0, -9, 13, 0, 0, 0, 0, 0 },
21638		{ 2, 0, 2, 0, 2, 0, 0, 2, 0, -3, 0, 0, 0, 0 },
21639
21640		/* 171-180 */
21641		{ 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -2 },
21642		{ 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 2, 0, 0, 0 },
21643		{ 1, 0, 0, -1, -1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
21644		{ 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -2 },
21645		{ 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 0 },
21646		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1 },
21647		{ 1, 0, 2, 0, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21648		{ 1, 0, -2, 0, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0 },
21649		{ 0, 0, 0, 0, 1, 0, 0, -2, 4, 0, 0, 0, 0, 0 },
21650		{ 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0 },
21651
21652		/* 181-190 */
21653		{ 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2 },
21654		{ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1 },
21655		{ 0, 0, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21656		{ 0, 0, 0, 0, 0, 0, 0, 1, -8, 3, 0, 0, 0, -2 },
21657		{ 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0, -2 },
21658		{ 0, 0, 0, 0, 0, 0, 0, 7, -8, 3, 0, 0, 0, 2 },
21659		{ 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0, 0, 0, 0 },
21660		{ 0, 0, 1, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0 },
21661		{ 0, 0, 1, -1, 0, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
21662		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 1 },
21663
21664		/* 191-200 */
21665		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -1, 0, 0, 0, 0 },
21666		{ 0, 0, 0, 0, 0, 0, 7,-10, 0, 0, 0, 0, 0, -2 },
21667		{ 1, 0, 0, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21668		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0 },
21669		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, -5, 0, 0, 0 },
21670		{ 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, -1 },
21671		{ 0, 0, 1, -1, 1, 0, 0, -9, 15, 0, 0, 0, 0, 0 },
21672		{ 0, 0, 0, 0, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0 },
21673		{ 0, 0, 0, 0, 1, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
21674		{ 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0 },
21675
21676		/* 201-210 */
21677		{ 0, 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, -2 },
21678		{ 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 2 },
21679		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -1, 0, 0, 2 },
21680		{ 2, 0, 0, -2, 1, 0, -6, 8, 0, 0, 0, 0, 0, 0 },
21681		{ 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, -1 },
21682		{ 0, 0, 1, -1, 1, 0, 3, -6, 0, 0, 0, 0, 0, 0 },
21683		{ 0, 0, 1, -1, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
21684		{ 0, 0, 1, -1, 1, 0, 8,-14, 0, 0, 0, 0, 0, 0 },
21685		{ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0 },
21686		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21687
21688		/* 211-220 */
21689		{ 0, 0, 0, 0, 1, 0, 0, 8,-15, 0, 0, 0, 0, 0 },
21690		{ 0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, 0 },
21691		{ 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, 0 },
21692		{ 2, 0, 0, -2, 1, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21693		{ 0, 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 2 },
21694		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2 },
21695		{ 2, 0, -1, -1, 0, 0, 0, 3, -7, 0, 0, 0, 0, 0 },
21696		{ 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -2 },
21697		{ 0, 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0 },
21698		{ 0, 0, 1, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
21699
21700		/* 221-230 */
21701		{ 2, 0, 0, -2, 0, 0, 0, -6, 8, 0, 0, 0, 0, 0 },
21702		{ 2, 0, 0, -2, 0, 0, 0, -5, 6, 0, 0, 0, 0, 0 },
21703		{ 0, 0, 0, 0, 1, 0, 0, 0, 0, -1, 0, 0, 0, 0 },
21704		{ 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1 },
21705		{ 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 1 },
21706		{ 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2 },
21707		{ 0, 0, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21708		{ 0, 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0 },
21709		{ 0, 0, 0, 0, 0, 0, 3, -9, 4, 0, 0, 0, 0, -2 },
21710		{ 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -2 },
21711
21712		/* 231-240 */
21713		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, -2 },
21714		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1 },
21715		{ 0, 0, 0, 0, 0, 0, 7,-11, 0, 0, 0, 0, 0, -2 },
21716		{ 0, 0, 0, 0, 0, 0, 3, -5, 4, 0, 0, 0, 0, 2 },
21717		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0 },
21718		{ 2, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21719		{ 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, -2 },
21720		{ 0, 0, 1, -1, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
21721		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2 },
21722		{ 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, -1 },
21723
21724		/* 241-250 */
21725		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 1, 0, 0, 0 },
21726		{ 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0, 0, 0, 1 },
21727		{ 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0 },
21728		{ 0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, 0 },
21729		{ 0, 0, 1, -1, 1, 0, 2, -4, 0, -3, 0, 0, 0, 0 },
21730		{ 0, 0, 0, 0, 1, 0, 3, -5, 0, 2, 0, 0, 0, 0 },
21731		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 2 },
21732		{ 0, 0, 2, -2, 2, 0, -8, 11, 0, 0, 0, 0, 0, 0 },
21733		{ 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 0 },
21734		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -2, 0, 0, 0 },
21735
21736		/* 251-260 */
21737		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2 },
21738		{ 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -2 },
21739		{ 0, 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 2 },
21740		{ 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 0, -1 },
21741		{ 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, 0, -1 },
21742		{ 0, 0, 0, 0, 0, 0, 2, -1, 0, 0, 0, 0, 0, 0 },
21743		{ 1, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21744		{ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2 },
21745		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 5, 0, 0, 2 },
21746		{ 0, 0, 0, 0, 0, 0, 3, -3, 0, 0, 0, 0, 0, 1 },
21747
21748		/* 261-270 */
21749		{ 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 2 },
21750		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, -5, 0, 0, 2 },
21751		{ 2, 0, 0, -2, -1, 0, 0, -2, 0, 0, 5, 0, 0, 0 },
21752		{ 2, 0, 0, -2, -1, 0, -6, 8, 0, 0, 0, 0, 0, 0 },
21753		{ 1, 0, 0, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21754		{ 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, 0 },
21755		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, -5, 0, 0, 2 },
21756		{ 0, 0, 0, 0, 1, 0, 3, -7, 4, 0, 0, 0, 0, 0 },
21757		{ 0, 0, 2, -2, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
21758		{ 0, 0, 0, 0, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21759
21760		/* 271-280 */
21761		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, -2, 5, 0, 0, 0 },
21762		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, -3, 0, 0, 0, 0 },
21763		{ 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 1 },
21764		{ 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, -2 },
21765		{ 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 2 },
21766		{ 0, 0, 0, 0, 0, 0, 0, 6,-15, 0, 0, 0, 0, -2 },
21767		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 2 },
21768		{ 1, 0, 0, -1, 0, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
21769		{ 0, 0, 0, 0, 1, 0, -3, 7, -4, 0, 0, 0, 0, 0 },
21770		{ 0, 0, 0, 0, 0, 0, 0, 5, 0, -2, 0, 0, 0, 2 },
21771
21772		/* 281-290 */
21773		{ 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, 0, 1 },
21774		{ 0, 0, 2, -2, 2, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21775		{ 0, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21776		{ 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2 },
21777		{ 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0 },
21778		{ 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 2 },
21779		{ 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, -2 },
21780		{ 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0 },
21781		{ 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0, 0 },
21782		{ 0, 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, -2 },
21783
21784		/* 291-300 */
21785		{ 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, -2 },
21786		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 3, 0, 0, 0, 0 },
21787		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21788		{ 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 1 },
21789		{ 0, 0, 0, 0, 0, 0, 9,-12, 0, 0, 0, 0, 0, -2 },
21790		{ 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0, 1 },
21791		{ 0, 0, 1, -1, 0, 0, -8, 12, 0, 0, 0, 0, 0, 0 },
21792		{ 0, 0, 1, -1, 1, 0, -2, 3, 0, 0, 0, 0, 0, 0 },
21793		{ 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 0, -1 },
21794		{ 0, 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, -1 },
21795
21796		/* 301-310 */
21797		{ 0, 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 2 },
21798		{ 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, -2 },
21799		{ 0, 0, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21800		{ 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, -1 },
21801		{ 0, 0, 1, -1, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21802		{ 0, 0, 0, 0, 0, 0, 0, 1, -5, 0, 0, 0, 0, -2 },
21803		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 3, -1, 0, 0, 0 },
21804		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0 },
21805		{ 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0 },
21806		{ 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 2 },
21807
21808		/* 311-320 */
21809		{ 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, -1 },
21810		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 3, 0, 0, 0 },
21811		{ 0, 0, 0, 0, 1, 0, 0, 2, -4, 0, 0, 0, 0, 0 },
21812		{ 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 2 },
21813		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1 },
21814		{ 0, 0, 1, -1, 2, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21815		{ 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, 0, -2 },
21816		{ 0, 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 2 },
21817		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 2 },
21818		{ 0, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21819
21820		/* 321-330 */
21821		{ 0, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21822		{ 0, 0, 0, 0, 0, 0, 0, 5, 0, -3, 0, 0, 0, 2 },
21823		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0 },
21824		{ 2, 0, -1, -1, -1, 0, 0, -1, 0, 3, 0, 0, 0, 0 },
21825		{ 0, 0, 0, 0, 0, 0, 4, -3, 0, 0, 0, 0, 0, 2 },
21826		{ 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 2 },
21827		{ 0, 0, 0, 0, 0, 0, 5,-10, 0, 0, 0, 0, 0, -2 },
21828		{ 0, 0, 0, 0, 0, 0, 8,-13, 0, 0, 0, 0, 0, 1 },
21829		{ 0, 0, 2, -2, 1, -1, 0, 2, 0, 0, 0, 0, 0, 0 },
21830		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 2, 0, 0 },
21831
21832		/* 331-340 */
21833		{ 0, 0, 0, 0, 1, 0, 3, -5, 0, 0, 0, 0, 0, 0 },
21834		{ 1, 0, 0, -2, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21835		{ 0, 0, 2, -2, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21836		{ 0, 0, 0, 0, 0, 0, 9, -9, 0, 0, 0, 0, 0, 0 },
21837		{ 0, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
21838		{ 0, 0, 2, -2, 1, 0, 0, -8, 11, 0, 0, 0, 0, 0 },
21839		{ 0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 2, 0, 0, 0 },
21840		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, -1, 2, 0, 0, 0 },
21841		{ 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 2 },
21842		{ 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, 0, -2 },
21843
21844		/* 341-350 */
21845		{ 0, 0, 0, 0, 0, 0, 0, 8,-15, 0, 0, 0, 0, -1 },
21846		{ 0, 0, 0, 0, 0, 0, 0, 5, -2, 0, 0, 0, 0, 2 },
21847		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2 },
21848		{ 0, 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, -2 },
21849		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, -2, 0, 0, 0, 0 },
21850		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 2 },
21851		{ 0, 0, 2, -2, 1, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21852		{ 0, 0, 0, 0, 0, 0, 8, -8, 0, 0, 0, 0, 0, -1 },
21853		{ 0, 0, 0, 0, 0, 0, 8,-10, 0, 0, 0, 0, 0, -1 },
21854		{ 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 1 },
21855
21856		/* 351-360 */
21857		{ 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, -1 },
21858		{ 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -1 },
21859		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 2 },
21860		{ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2 },
21861		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -4, 0, 0, 0, 0 },
21862		{ 2, 0, 0, -2, -1, 0, 0, -5, 6, 0, 0, 0, 0, 0 },
21863		{ 0, 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, -2 },
21864		{ 2, 0, -1, -1, -1, 0, 0, 3, -7, 0, 0, 0, 0, 0 },
21865		{ 0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, 0 },
21866		{ 0, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
21867
21868		/* 361-370 */
21869		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 4, -3, 0, 0, 0 },
21870		{ 0, 0, 0, 0, 0, 0, 0, 6,-11, 0, 0, 0, 0, 0 },
21871		{ 2, 0, 0, -2, 1, 0, 0, -6, 8, 0, 0, 0, 0, 0 },
21872		{ 0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, -2 },
21873		{ 0, 0, 0, 0, 0, 0, 0, 6, -5, 0, 0, 0, 0, 2 },
21874		{ 1, 0, -2, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21875		{ 0, 0, 1, -1, 2, 0, 0, 0, -2, 0, 0, 0, 0, 0 },
21876		{ 0, 0, 0, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21877		{ 0, 0, 0, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21878		{ 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 1 },
21879
21880		/* 371-380 */
21881		{ 0, 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 2 },
21882		{ 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, -2, 0, 0, 2 },
21883		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, -2, 0, 0, 2 },
21884		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1 },
21885		{ 0, 0, 0, 0, 0, 0, 0, 1, -6, 0, 0, 0, 0, -2 },
21886		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 2 },
21887		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2 },
21888		{ 0, 0, 0, 0, 0, 0, 3, -5, 0, 2, 0, 0, 0, 0 },
21889		{ 0, 0, 0, 0, 0, 0, 0, 7,-13, 0, 0, 0, 0, 0 },
21890		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2 },
21891
21892		/* 381-390 */
21893		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 2, 0, 0, 0 },
21894		{ 0, 0, 0, 0, 1, 0, 0, -8, 15, 0, 0, 0, 0, 0 },
21895		{ 2, 0, 0, -2, -2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21896		{ 2, 0, -1, -1, -1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21897		{ 1, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21898		{ 1, 0, -1, 1, -1, 0,-18, 17, 0, 0, 0, 0, 0, 0 },
21899		{ 0, 0, 2, 0, 2, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21900		{ 0, 0, 2, 0, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21901		{ 0, 0, 2, -2, -1, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21902		{ 0, 0, 1, -1, 2, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21903
21904		/* 391-400 */
21905		{ 0, 0, 0, 0, 1, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
21906		{ 0, 0, 0, 0, 0, 0, 8,-16, 0, 0, 0, 0, 0, -2 },
21907		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 2 },
21908		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2 },
21909		{ 0, 0, 0, 0, 2, 0, 0, -1, 2, 0, 0, 0, 0, 0 },
21910		{ 2, 0, -1, -1, -2, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
21911		{ 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0, -1 },
21912		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, -2, 4, 0, 0, 0 },
21913		{ 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 2 },
21914		{ 2, 0, 0, -2, -1, 0, 0, -2, 0, 4, -5, 0, 0, 0 },
21915
21916		/* 401-410 */
21917		{ 2, 0, 0, -2, -1, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
21918		{ 2, 0, -1, -1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0 },
21919		{ 1, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 0, 0 },
21920		{ 1, 0, 0, -1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
21921		{ 1, 0, -1, -1, -1, 0, 20,-20, 0, 0, 0, 0, 0, 0 },
21922		{ 0, 0, 2, -2, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21923		{ 0, 0, 1, -1, 1, 0, 1, -2, 0, 0, 0, 0, 0, 0 },
21924		{ 0, 0, 1, -1, 1, 0, -2, 1, 0, 0, 0, 0, 0, 0 },
21925		{ 0, 0, 0, 0, 1, 0, 5, -8, 0, 0, 0, 0, 0, 0 },
21926		{ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0 },
21927
21928		/* 411-420 */
21929		{ 0, 0, 0, 0, 0, 0, 9,-11, 0, 0, 0, 0, 0, -1 },
21930		{ 0, 0, 0, 0, 0, 0, 5, -3, 0, 0, 0, 0, 0, 1 },
21931		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 0, 0, 0, -1 },
21932		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1 },
21933		{ 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, 0 },
21934		{ 0, 0, 0, 0, 0, 0, 0, 3, -2, 0, 0, 0, 0, 0 },
21935		{ 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -2 },
21936		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, -2, 0, 0, 0 },
21937		{ 0, 0, 1, -1, 2, 0, 0, -1, 0, -2, 5, 0, 0, 0 },
21938		{ 0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, 0 },
21939
21940		/* 421-430 */
21941		{ 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0, 0 },
21942		{ 0, 0, 0, 0, 0, 0, 0, 5, -8, 0, 0, 0, 0, -2 },
21943		{ 0, 0, 0, 0, 0, 0, 0, 2, -6, 0, 0, 0, 0, -2 },
21944		{ 1, 0, 0, -2, 0, 0, 20,-21, 0, 0, 0, 0, 0, 0 },
21945		{ 0, 0, 0, 0, 0, 0, 8,-12, 0, 0, 0, 0, 0, 0 },
21946		{ 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, 0 },
21947		{ 0, 0, 0, 0, 0, 0, 0, 4, -4, 0, 0, 0, 0, 0 },
21948		{ 0, 0, 1, -1, 2, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21949		{ 0, 0, 0, 0, 0, 0, 8,-12, 0, 0, 0, 0, 0, -2 },
21950		{ 0, 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, 0 },
21951
21952		/* 431-440 */
21953		{ 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 2 },
21954		{ 0, 0, 0, 0, 0, 0, 0, 4, -8, 1, 5, 0, 0, 2 },
21955		{ 0, 0, 0, 0, 0, 0, 0, 4, -6, 0, 0, 0, 0, -2 },
21956		{ 0, 0, 0, 0, 0, 0, 0, 2, -7, 0, 0, 0, 0, -2 },
21957		{ 1, 0, 0, -1, 1, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
21958		{ 1, 0, -2, 0, -2, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
21959		{ 0, 0, 0, 0, 1, 0, 0, -9, 17, 0, 0, 0, 0, 0 },
21960		{ 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -2 },
21961		{ 1, 0, -2, -2, -2, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
21962		{ 1, 0, -1, 1, -1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21963
21964		/* 441-450 */
21965		{ 0, 0, 2, -2, 2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
21966		{ 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, 1, 0, 0, 0 },
21967		{ 0, 0, 1, -1, 2, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
21968		{ 0, 0, 0, 0, 1, 0, 0, 2, -2, 0, 0, 0, 0, 0 },
21969		{ 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -1 },
21970		{ 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, -2 },
21971		{ 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 0, 0 },
21972		{ 0, 0, 0, 0, 0, 0, 0, 5,-10, 0, 0, 0, 0, -2 },
21973		{ 0, 0, 0, 0, 0, 0, 0, 4, 0, -4, 0, 0, 0, 2 },
21974		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, -5, 0, 0, 0, -2 },
21975
21976		/* 451-460 */
21977		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -5, 0, 0, 0, -2 },
21978		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 5, 0, 0, 2 },
21979		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -2 },
21980		{ 0, 0, 0, 0, 0, 0, 2, -3, 0, 0, 0, 0, 0, 1 },
21981		{ 1, 0, 0, -2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21982		{ 0, 0, 0, 0, 0, 0, 3, -7, 4, 0, 0, 0, 0, 0 },
21983		{ 2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
21984		{ 0, 0, 1, -1, -1, 0, 0, -1, 0, -1, 0, 0, 0, 0 },
21985		{ 0, 0, 0, 0, 1, 0, 0, 1, 0, -2, 0, 0, 0, 0 },
21986		{ 0, 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, -2 },
21987
21988		/* 461-470 */
21989		{ 1, 0, 0, -1, 1, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
21990		{ 0, 0, 2, -2, 1, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
21991		{ 0, 0, 2, -2, 1, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
21992		{ 0, 0, 2, -2, 1, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
21993		{ 0, 0, 2, -2, 1, 0, 0, -3, 0, 3, 0, 0, 0, 0 },
21994		{ 0, 0, 2, -2, 1, 0, -5, 5, 0, 0, 0, 0, 0, 0 },
21995		{ 0, 0, 1, -1, 1, 0, 1, -3, 0, 0, 0, 0, 0, 0 },
21996		{ 0, 0, 1, -1, 1, 0, 0, -4, 6, 0, 0, 0, 0, 0 },
21997		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 0, 0, -1, 0, 0 },
21998		{ 0, 0, 1, -1, 1, 0, -5, 6, 0, 0, 0, 0, 0, 0 },
21999
22000		/* 471-480 */
22001		{ 0, 0, 0, 0, 1, 0, 3, -4, 0, 0, 0, 0, 0, 0 },
22002		{ 0, 0, 0, 0, 1, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22003		{ 0, 0, 0, 0, 0, 0, 7,-10, 0, 0, 0, 0, 0, -1 },
22004		{ 0, 0, 0, 0, 0, 0, 5, -5, 0, 0, 0, 0, 0, 1 },
22005		{ 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, -2 },
22006		{ 0, 0, 0, 0, 0, 0, 3, -8, 0, 0, 0, 0, 0, -2 },
22007		{ 0, 0, 0, 0, 0, 0, 2, -5, 0, 0, 0, 0, 0, -1 },
22008		{ 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, -1 },
22009		{ 0, 0, 0, 0, 0, 0, 0, 7, -9, 0, 0, 0, 0, 2 },
22010		{ 0, 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 2 },
22011
22012		/* 481-490 */
22013		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2 },
22014		{ 0, 0, 0, 0, 0, 0, 0, 3, -8, 3, 0, 0, 0, -2 },
22015		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 1 },
22016		{ 0, 0, 0, 0, 0, 0, 0, 2, -4, 0, 0, 0, 0, 1 },
22017		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1 },
22018		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1 },
22019		{ 2, 0, 0, -2, -1, 0, 0, -6, 8, 0, 0, 0, 0, 0 },
22020		{ 2, 0, -1, -1, 1, 0, 0, 3, -7, 0, 0, 0, 0, 0 },
22021		{ 0, 0, 2, -2, 1, 0, 0, -7, 9, 0, 0, 0, 0, 0 },
22022		{ 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0, 0, -1 },
22023
22024		/* 491-500 */
22025		{ 0, 0, 1, -1, 2, 0, -8, 12, 0, 0, 0, 0, 0, 0 },
22026		{ 1, 0, 0, 0, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22027		{ 1, 0, 0, -2, 0, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
22028		{ 0, 0, 0, 0, 0, 0, 7, -8, 0, 0, 0, 0, 0, 0 },
22029		{ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0 },
22030		{ 2, 0, 0, -2, 1, 0, 0, -5, 6, 0, 0, 0, 0, 0 },
22031		{ 2, 0, 0, -2, -1, 0, 0, -2, 0, 3, -1, 0, 0, 0 },
22032		{ 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22033		{ 1, 0, 0, -2, 1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22034		{ 1, 0, 0, -2, -1, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22035
22036		/* 501-510 */
22037		{ 1, 0, 0, -1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0 },
22038		{ 1, 0, -1, 0, -1, 0, -3, 5, 0, 0, 0, 0, 0, 0 },
22039		{ 0, 0, 2, -2, 1, 0, 0, -4, 4, 0, 0, 0, 0, 0 },
22040		{ 0, 0, 2, -2, 1, 0, 0, -2, 0, 0, 0, 0, 0, 0 },
22041		{ 0, 0, 2, -2, 1, 0, -8, 11, 0, 0, 0, 0, 0, 0 },
22042		{ 0, 0, 2, -2, 0, 0, 0, -9, 13, 0, 0, 0, 0, 0 },
22043		{ 0, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22044		{ 0, 0, 1, -1, 1, 0, 0, 1, -4, 0, 0, 0, 0, 0 },
22045		{ 0, 0, 1, -1, 1, 0, 0, -1, 0, 1, -3, 0, 0, 0 },
22046		{ 0, 0, 0, 0, 1, 0, 0, 7,-13, 0, 0, 0, 0, 0 },
22047
22048		/* 511-520 */
22049		{ 0, 0, 0, 0, 1, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22050		{ 0, 0, 0, 0, 1, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
22051		{ 0, 0, 0, 0, 1, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
22052		{ 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0, 0, 0 },
22053		{ 0, 0, 0, 0, 0, 0, 7,-11, 0, 0, 0, 0, 0, -1 },
22054		{ 0, 0, 0, 0, 0, 0, 6, -6, 0, 0, 0, 0, 0, 1 },
22055		{ 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 0, 1 },
22056		{ 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -1 },
22057		{ 0, 0, 0, 0, 0, 0, 4, -2, 0, 0, 0, 0, 0, 0 },
22058		{ 0, 0, 0, 0, 0, 0, 3, -4, 0, 0, 0, 0, 0, 1 },
22059
22060		/* 521-530 */
22061		{ 0, 0, 0, 0, 0, 0, 1, -4, 0, 0, 0, 0, 0, -1 },
22062		{ 0, 0, 0, 0, 0, 0, 0, 9,-17, 0, 0, 0, 0, -2 },
22063		{ 0, 0, 0, 0, 0, 0, 0, 7, -7, 0, 0, 0, 0, 2 },
22064		{ 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 1 },
22065		{ 0, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, -1 },
22066		{ 0, 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0 },
22067		{ 0, 0, 0, 0, 0, 0, 0, 4, -7, 0, 0, 0, 0, -1 },
22068		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1 },
22069		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -4, 0, 0, 0, 0 },
22070		{ 2, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22071
22072		/* 531-540 */
22073		{ 2, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22074		{ 1, 0, 0, 0, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
22075		{ 1, 0, 0, 0, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22076		{ 1, 0, 0, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
22077		{ 1, 0, 0, -2, 0, 0, 17,-16, 0, -2, 0, 0, 0, 0 },
22078		{ 1, 0, 0, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
22079		{ 0, 0, 2, -2, 0, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22080		{ 0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0 },
22081		{ 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0 },
22082		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, -4, 0, 0, 0, 0 },
22083
22084		/* 541-550 */
22085		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2 },
22086		{ 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2 },
22087		{ 2, 0, 0, -2, 0, 0, 0, -4, 4, 0, 0, 0, 0, 0 },
22088		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 2, 2, 0, 0, 0 },
22089		{ 1, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22090		{ 1, 0, 0, 0, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
22091		{ 1, 0, 0, 0, 0, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
22092		{ 1, 0, 0, -2, 0, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22093		{ 1, 0, 0, -2, 0, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
22094		{ 1, 0, 0, -2, 0, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22095
22096		/* 551-560 */
22097		{ 1, 0, 0, -2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22098		{ 0, 0, 2, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0 },
22099		{ 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22100		{ 0, 0, 1, -1, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0 },
22101		{ 0, 0, 1, -1, 0, 0, 0, -2, 2, 0, 0, 0, 0, 0 },
22102		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
22103		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, 1, 0, 0, 0 },
22104		{ 0, 0, 1, -1, 0, 0, -4, 5, 0, 0, 0, 0, 0, 0 },
22105		{ 0, 0, 1, -1, 0, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
22106		{ 0, 0, 0, 2, 0, 0, 0, -1, 0, 1, 0, 0, 0, 0 },
22107
22108		/* 561-570 */
22109		{ 0, 0, 0, 0, 0, 0, 8, -9, 0, 0, 0, 0, 0, 0 },
22110		{ 0, 0, 0, 0, 0, 0, 3, -6, 0, 0, 0, 0, 0, 0 },
22111		{ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0 },
22112		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, -5, 0, 0, 0 },
22113		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -2, 0, 0, 0 },
22114		{ 2, 0, -2, -2, -2, 0, 0, -2, 0, 2, 0, 0, 0, 0 },
22115		{ 1, 0, 0, 0, 1, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
22116		{ 1, 0, 0, 0, -1, 0,-10, 3, 0, 0, 0, 0, 0, 0 },
22117		{ 0, 0, 2, 0, 2, 0, 2, -3, 0, 0, 0, 0, 0, 0 },
22118		{ 0, 0, 2, 0, 2, 0, 2, -2, 0, 0, 0, 0, 0, 0 },
22119
22120		/* 571-580 */
22121		{ 0, 0, 2, 0, 2, 0, -2, 3, 0, 0, 0, 0, 0, 0 },
22122		{ 0, 0, 2, 0, 2, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22123		{ 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0 },
22124		{ 0, 0, 0, 0, 1, 0, 0, -1, 0, 2, 0, 0, 0, 0 },
22125		{ 2, 0, 2, -2, 2, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
22126		{ 2, 0, 1, -3, 1, 0, -6, 7, 0, 0, 0, 0, 0, 0 },
22127		{ 2, 0, 0, -2, 0, 0, 2, -5, 0, 0, 0, 0, 0, 0 },
22128		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 5, -5, 0, 0, 0 },
22129		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 1, 5, 0, 0, 0 },
22130		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 5, 0, 0, 0 },
22131
22132		/* 581-590 */
22133		{ 2, 0, 0, -2, 0, 0, 0, -2, 0, 0, 2, 0, 0, 0 },
22134		{ 2, 0, 0, -2, 0, 0, -4, 4, 0, 0, 0, 0, 0, 0 },
22135		{ 2, 0, -2, 0, -2, 0, 0, 5, -9, 0, 0, 0, 0, 0 },
22136		{ 2, 0, -1, -1, 0, 0, 0, -1, 0, 3, 0, 0, 0, 0 },
22137		{ 1, 0, 2, 0, 2, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22138		{ 1, 0, 2, 0, 2, 0, 0, 4, -8, 3, 0, 0, 0, 0 },
22139		{ 1, 0, 2, 0, 2, 0, 0, -4, 8, -3, 0, 0, 0, 0 },
22140		{ 1, 0, 2, 0, 2, 0, -1, 1, 0, 0, 0, 0, 0, 0 },
22141		{ 1, 0, 2, -2, 2, 0, -3, 3, 0, 0, 0, 0, 0, 0 },
22142		{ 1, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
22143
22144		/* 591-600 */
22145		{ 1, 0, 0, 0, 0, 0, 0, -2, 0, 3, 0, 0, 0, 0 },
22146		{ 1, 0, 0, -2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22147		{ 1, 0, -2, -2, -2, 0, 0, 1, 0, -1, 0, 0, 0, 0 },
22148		{ 1, 0, -1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22149		{ 1, 0, -1, -1, 0, 0, 0, 8,-15, 0, 0, 0, 0, 0 },
22150		{ 0, 0, 2, 2, 2, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22151		{ 0, 0, 2, -2, 1, 0, 1, -1, 0, 0, 0, 0, 0, 0 },
22152		{ 0, 0, 2, -2, 1, 0, 0, -2, 0, 1, 0, 0, 0, 0 },
22153		{ 0, 0, 2, -2, 1, 0, 0,-10, 15, 0, 0, 0, 0, 0 },
22154		{ 0, 0, 2, -2, 0, -1, 0, 2, 0, 0, 0, 0, 0, 0 },
22155
22156		/* 601-610 */
22157		{ 0, 0, 1, -1, 2, 0, 0, -1, 0, 0, -1, 0, 0, 0 },
22158		{ 0, 0, 1, -1, 2, 0, -3, 4, 0, 0, 0, 0, 0, 0 },
22159		{ 0, 0, 1, -1, 1, 0, -4, 6, 0, 0, 0, 0, 0, 0 },
22160		{ 0, 0, 1, -1, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0 },
22161		{ 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0 },
22162		{ 0, 0, 1, -1, 0, 0, 0, -1, 0, 0, -2, 0, 0, 0 },
22163		{ 0, 0, 1, -1, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22164		{ 0, 0, 1, -1, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0 },
22165		{ 0, 0, 1, -1, -1, 0, -5, 7, 0, 0, 0, 0, 0, 0 },
22166		{ 0, 0, 0, 2, 0, 0, 0, 2, 0, -2, 0, 0, 0, 0 },
22167
22168		/* 611-620 */
22169		{ 0, 0, 0, 2, 0, 0, -2, 2, 0, 0, 0, 0, 0, 0 },
22170		{ 0, 0, 0, 0, 2, 0, -3, 5, 0, 0, 0, 0, 0, 0 },
22171		{ 0, 0, 0, 0, 1, 0, -1, 2, 0, 0, 0, 0, 0, 0 },
22172		{ 0, 0, 0, 0, 0, 0, 9,-13, 0, 0, 0, 0, 0, -2 },
22173		{ 0, 0, 0, 0, 0, 0, 8,-14, 0, 0, 0, 0, 0, -2 },
22174		{ 0, 0, 0, 0, 0, 0, 8,-11, 0, 0, 0, 0, 0, -1 },
22175		{ 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, 0, 0 },
22176		{ 0, 0, 0, 0, 0, 0, 6, -8, 0, 0, 0, 0, 0, 0 },
22177		{ 0, 0, 0, 0, 0, 0, 6, -7, 0, 0, 0, 0, 0, -1 },
22178		{ 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0, -2 },
22179
22180		/* 621-630 */
22181		{ 0, 0, 0, 0, 0, 0, 5, -6, -4, 0, 0, 0, 0, -2 },
22182		{ 0, 0, 0, 0, 0, 0, 5, -4, 0, 0, 0, 0, 0, 2 },
22183		{ 0, 0, 0, 0, 0, 0, 4, -8, 0, 0, 0, 0, 0, -2 },
22184		{ 0, 0, 0, 0, 0, 0, 4, -5, 0, 0, 0, 0, 0, 0 },
22185		{ 0, 0, 0, 0, 0, 0, 3, -3, 0, 2, 0, 0, 0, 2 },
22186		{ 0, 0, 0, 0, 0, 0, 3, -1, 0, 0, 0, 0, 0, 0 },
22187		{ 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0 },
22188		{ 0, 0, 0, 0, 0, 0, 1, -1, 0, 0, 0, 0, 0, -2 },
22189		{ 0, 0, 0, 0, 0, 0, 0, 7,-12, 0, 0, 0, 0, -2 },
22190		{ 0, 0, 0, 0, 0, 0, 0, 6, -9, 0, 0, 0, 0, -2 },
22191
22192		/* 631-640 */
22193		{ 0, 0, 0, 0, 0, 0, 0, 6, -8, 1, 5, 0, 0, 2 },
22194		{ 0, 0, 0, 0, 0, 0, 0, 6, -4, 0, 0, 0, 0, 2 },
22195		{ 0, 0, 0, 0, 0, 0, 0, 6,-10, 0, 0, 0, 0, 0 },
22196		{ 0, 0, 0, 0, 0, 0, 0, 5, 0, -4, 0, 0, 0, 2 },
22197		{ 0, 0, 0, 0, 0, 0, 0, 5, -9, 0, 0, 0, 0, -1 },
22198		{ 0, 0, 0, 0, 0, 0, 0, 5, -8, 3, 0, 0, 0, 2 },
22199		{ 0, 0, 0, 0, 0, 0, 0, 5, -7, 0, 0, 0, 0, -2 },
22200		{ 0, 0, 0, 0, 0, 0, 0, 5, -6, 0, 0, 0, 0, 0 },
22201		{ 0, 0, 0, 0, 0, 0, 0, 5,-16, 4, 5, 0, 0, -2 },
22202		{ 0, 0, 0, 0, 0, 0, 0, 5,-13, 0, 0, 0, 0, -2 },
22203
22204		/* 641-650 */
22205		{ 0, 0, 0, 0, 0, 0, 0, 3, 0, -5, 0, 0, 0, -2 },
22206		{ 0, 0, 0, 0, 0, 0, 0, 3, -9, 0, 0, 0, 0, -2 },
22207		{ 0, 0, 0, 0, 0, 0, 0, 3, -7, 0, 0, 0, 0, -2 },
22208		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 2 },
22209		{ 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -3, 0, 0, 0 },
22210		{ 0, 0, 0, 0, 0, 0, 0, 2, -8, 1, 5, 0, 0, -2 },
22211		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, -5, 0, 0, 0 },
22212		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2 },
22213		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, -3, 0, 0, 0 },
22214		{ 0, 0, 0, 0, 0, 0, 0, 1, 0, -3, 5, 0, 0, 0 },
22215
22216		/* 651-NFPL */
22217		{ 0, 0, 0, 0, 0, 0, 0, 1, -3, 0, 0, 0, 0, 0 },
22218		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, -6, 3, 0, -2 },
22219		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 0, 0, 0 },
22220		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 },
22221		{ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 },
22222		{ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 }
22223		};
22224
22225		/**
22226		*
22227		* Time scale transformation: Terrestrial Time, TT, to International
22228		* Atomic Time, TAI.
22229		*
22230		* <p>This function is derived from the International Astronomical Union's
22231		* SOFA (Standards of Fundamental Astronomy) software collection.
22232		*
22233		*<p>Status: canonical.
22234		*
22235		*<!-- Given: -->
22236		* tt1,tt2 double TT as a 2-part Julian Date
22237		*
22238		*<!-- Returned:-->
22239		* tai1,tai2 double TAI as a 2-part Julian Date
22240		*
22241		* Returned (function value):
22242		* int status: 0 = OK
22243		*
22244		* Note:
22245		*
22246		* tt1+tt2 is Julian Date, apportioned in any convenient way between
22247		* the two arguments, for example where tt1 is the Julian Day Number
22248		* and tt2 is the fraction of a day. The returned tai1,tai2 follow
22249		* suit.
22250		*
22251		*<p>References:
22252		*
22253		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22254		* IERS Technical Note No. 32, BKG (2004)
22255		*
22256		* Explanatory Supplement to the Astronomical Almanac,
22257		* P. Kenneth Seidelmann (ed), University Science Books (1992)
22258		*
22259		*@version 2010 May 13
22260		*
22261		*@since SOFA release 2010-12-01
22262		*
22263		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22264		*/
22265		public static JulianDate jauTttai(double tt1, double tt2)
22266		{
22267		double tai1, tai2;
22268		/* TT minus TAI (days). */
22269	2	final double dtat = TTMTAI / 86400.0;
22270
22271
22272		/* Result, safeguarding precision. */
22273	2	if ( tt1 > tt2 ) {
22274	2	tai1 = tt1;
22275	2	tai2 = tt2 - dtat;
22276		} else {
22277	0	tai1 = tt1 - dtat;
22278	0	tai2 = tt2;
22279		}
22280
22281	2	return new JulianDate(tai1, tai2);
22282
22283		};
22284
22285		/**
22286		*
22287		* Time scale transformation: Terrestrial Time, TT, to Geocentric
22288		* Coordinate Time, TCG.
22289		*
22290		* <p>This function is derived from the International Astronomical Union's
22291		* SOFA (Standards of Fundamental Astronomy) software collection.
22292		*
22293		*<p>Status: canonical.
22294		*
22295		*<!-- Given: -->
22296		* tt1,tt2 double TT as a 2-part Julian Date
22297		*
22298		*<!-- Returned:-->
22299		* tcg1,tcg2 double TCG as a 2-part Julian Date
22300		*
22301		* Returned (function value):
22302		* int status: 0 = OK
22303		*
22304		* Note:
22305		*
22306		* tt1+tt2 is Julian Date, apportioned in any convenient way between
22307		* the two arguments, for example where tt1 is the Julian Day Number
22308		* and tt2 is the fraction of a day. The returned tcg1,tcg2 follow
22309		* suit.
22310		*
22311		*<p>References:
22312		*
22313		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22314		* IERS Technical Note No. 32, BKG (2004)
22315		*
22316		* IAU 2000 Resolution B1.9
22317		*
22318		*@version 2010 May 13
22319		*
22320		*@since SOFA release 2010-12-01
22321		*
22322		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22323		*/
22324		public static JulianDate jauTttcg(double tt1, double tt2)
22325
22326		{
22327		double tcg1, tcg2;
22328
22329		/* 1977 Jan 1 00:00:32.184 TT, as MJD */
22330	2	final double t77t = DJM77 + TTMTAI/DAYSEC;
22331
22332		/* TT to TCG rate */
22333	2	final double elgg = ELG/(1.0-ELG);
22334
22335
22336		/* Result, safeguarding precision. */
22337	2	if ( tt1 > tt2 ) {
22338	2	tcg1 = tt1;
22339	2	tcg2 = tt2 + ( ( tt1 - DJM0 ) + ( tt2 - t77t ) ) * elgg;
22340		} else {
22341	0	tcg1 = tt1 + ( ( tt2 - DJM0 ) + ( tt1 - t77t ) ) * elgg;
22342	0	tcg2 = tt2;
22343		}
22344
22345	2	return new JulianDate(tcg1, tcg2);
22346
22347		};
22348
22349		/**
22350		*
22351		* Time scale transformation: Terrestrial Time, TT, to Barycentric
22352		* Dynamical Time, TDB.
22353		*
22354		* <p>This function is derived from the International Astronomical Union's
22355		* SOFA (Standards of Fundamental Astronomy) software collection.
22356		*
22357		*<p>Status: canonical.
22358		*
22359		*<!-- Given: -->
22360		* tt1,tt2 double TT as a 2-part Julian Date
22361		* dtr double TDB-TT in seconds
22362		*
22363		*<!-- Returned:-->
22364		* tdb1,tdb2 double TDB as a 2-part Julian Date
22365		*
22366		* Returned (function value):
22367		* int status: 0 = OK
22368		*
22369		*<p>Notes:
22370		*
22371		* 1 tt1+tt2 is Julian Date, apportioned in any convenient way between
22372		* the two arguments, for example where tt1 is the Julian Day Number
22373		* and tt2 is the fraction of a day. The returned tdb1,tdb2 follow
22374		* suit.
22375		*
22376		* 2 The argument dtr represents the quasi-periodic component of the
22377		* GR transformation between TT and TCB. It is dependent upon the
22378		* adopted solar-system ephemeris, and can be obtained by numerical
22379		* integration, by interrogating a precomputed time ephemeris or by
22380		* evaluating a model such as that implemented in the SOFA function
22381		* jauDtdb. The quantity is dominated by an annual term of 1.7 ms
22382		* amplitude.
22383		*
22384		* 3 TDB is essentially the same as Teph, the time argument for the JPL
22385		* solar system ephemerides.
22386		*
22387		*<p>References:
22388		*
22389		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22390		* IERS Technical Note No. 32, BKG (2004)
22391		*
22392		* IAU 2006 Resolution 3
22393		*
22394		*@version 2010 May 13
22395		*
22396		*@since SOFA release 2010-12-01
22397		*
22398		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22399		*/
22400		public static JulianDate jauTttdb(double tt1, double tt2, double dtr)
22401		{
22402
22403		double tdb1, tdb2;
22404		double dtrd;
22405
22406
22407		/* Result, safeguarding precision. */
22408	2	dtrd = dtr / DAYSEC;
22409	2	if ( tt1 > tt2 ) {
22410	2	tdb1 = tt1;
22411	2	tdb2 = tt2 + dtrd;
22412		} else {
22413	0	tdb1 = tt1 + dtrd;
22414	0	tdb2 = tt2;
22415		}
22416
22417	2	return new JulianDate(tdb1, tdb2);
22418
22419		};
22420
22421		/**
22422		*
22423		* Time scale transformation: Terrestrial Time, TT, to Universal Time,
22424		* UT1.
22425		*
22426		* <p>This function is derived from the International Astronomical Union's
22427		* SOFA (Standards of Fundamental Astronomy) software collection.
22428		*
22429		*<p>Status: canonical.
22430		*
22431		*<!-- Given: -->
22432		* tt1,tt2 double TT as a 2-part Julian Date
22433		* dt double TT-UT1 in seconds
22434		*
22435		*<!-- Returned:-->
22436		* ut11,ut12 double UT1 as a 2-part Julian Date
22437		*
22438		* Returned (function value):
22439		* int status: 0 = OK
22440		*
22441		*<p>Notes:
22442		*
22443		* 1 tt1+tt2 is Julian Date, apportioned in any convenient way between
22444		* the two arguments, for example where tt1 is the Julian Day Number
22445		* and tt2 is the fraction of a day. The returned ut11,ut12 follow
22446		* suit.
22447		*
22448		* 2 The argument dt is classical Delta T.
22449		*
22450		* Reference:
22451		*
22452		* Explanatory Supplement to the Astronomical Almanac,
22453		* P. Kenneth Seidelmann (ed), University Science Books (1992)
22454		*
22455		*@version 2010 May 16
22456		*
22457		*@since SOFA release 2010-12-01
22458		*
22459		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22460		*/
22461		public static JulianDate jauTtut1(double tt1, double tt2, double dt)
22462
22463		{
22464
22465		double ut11, ut12;
22466		double dtd;
22467
22468
22469		/* Result, safeguarding precision. */
22470	2	dtd = dt / DAYSEC;
22471	2	if ( tt1 > tt2 ) {
22472	2	ut11 = tt1;
22473	2	ut12 = tt2 - dtd;
22474		} else {
22475	0	ut11 = tt1 - dtd;
22476	0	ut12 = tt2;
22477		}
22478
22479	2	return new JulianDate(ut11, ut12);
22480		};
22481
22482		/**
22483		*
22484		* Time scale transformation: Universal Time, UT1, to International
22485		* Atomic Time, TAI.
22486		*
22487		* <p>This function is derived from the International Astronomical Union's
22488		* SOFA (Standards of Fundamental Astronomy) software collection.
22489		*
22490		*<p>Status: canonical.
22491		*
22492		*<!-- Given: -->
22493		* ut11,ut12 double UT1 as a 2-part Julian Date
22494		* dta double UT1-TAI in seconds
22495		*
22496		*<!-- Returned:-->
22497		* tai1,tai2 double TAI as a 2-part Julian Date
22498		*
22499		* Returned (function value):
22500		* int status: 0 = OK
22501		*
22502		*<p>Notes:
22503		*
22504		* 1 ut11+ut12 is Julian Date, apportioned in any convenient way
22505		* between the two arguments, for example where ut11 is the Julian
22506		* Day Number and ut12 is the fraction of a day. The returned
22507		* TAI1,TAI2 follow suit.
22508		*
22509		* 2 The argument dta, i.e. UT1-TAI, is an observed quantity, and is
22510		* available from IERS tabulations.
22511		*
22512		* Reference:
22513		*
22514		* Explanatory Supplement to the Astronomical Almanac,
22515		* P. Kenneth Seidelmann (ed), University Science Books (1992)
22516		*
22517		*@version 2010 May 16
22518		*
22519		*@since SOFA release 2010-12-01
22520		*
22521		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22522		*/
22523		public static JulianDate jauUt1tai(double ut11, double ut12, double dta )
22524
22525		{
22526		double tai1, tai2;
22527		double dtad;
22528
22529
22530		/* Result, safeguarding precision. */
22531	2	dtad = dta / DAYSEC;
22532	2	if ( ut11 > ut12 ) {
22533	2	tai1 = ut11;
22534	2	tai2 = ut12 - dtad;
22535		} else {
22536	0	tai1 = ut11 - dtad;
22537	0	tai2 = ut12;
22538		}
22539	2	return new JulianDate(tai1, tai2);
22540
22541		};
22542
22543		/**
22544		*
22545		* Time scale transformation: Universal Time, UT1, to Terrestrial
22546		* Time, TT.
22547		*
22548		* <p>This function is derived from the International Astronomical Union's
22549		* SOFA (Standards of Fundamental Astronomy) software collection.
22550		*
22551		*<p>Status: canonical.
22552		*
22553		*<!-- Given: -->
22554		* ut11,ut12 double UT1 as a 2-part Julian Date
22555		* dt double TT-UT1 in seconds
22556		*
22557		*<!-- Returned:-->
22558		* tt1,tt2 double TAI as a 2-part Julian Date
22559		*
22560		* Returned (function value):
22561		* int status: 0 = OK
22562		*
22563		*<p>Notes:
22564		*
22565		* 1 ut11+ut12 is Julian Date, apportioned in any convenient way
22566		* between the two arguments, for example where ut11 is the Julian
22567		* Day Number and ut12 is the fraction of a day. The returned
22568		* tt1,tt2 follow suit.
22569		*
22570		* 2 The argument dt is classical Delta T.
22571		*
22572		* Reference:
22573		*
22574		* Explanatory Supplement to the Astronomical Almanac,
22575		* P. Kenneth Seidelmann (ed), University Science Books (1992)
22576		*
22577		*@version 2010 May 16
22578		*
22579		*@since SOFA release 2010-12-01
22580		*
22581		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22582		*/
22583		public static JulianDate jauUt1tt(double ut11, double ut12, double dt)
22584		{
22585
22586		double tt1, tt2;
22587		double dtd;
22588
22589
22590		/* Result, safeguarding precision. */
22591	2	dtd = dt / DAYSEC;
22592	2	if ( ut11 > ut12 ) {
22593	2	tt1 = ut11;
22594	2	tt2 = ut12 + dtd;
22595		} else {
22596	0	tt1 = ut11 + dtd;
22597	0	tt2 = ut12;
22598		}
22599
22600	2	return new JulianDate(tt1, tt2);
22601
22602		};
22603
22604		/**
22605		*
22606		* Time scale transformation: Universal Time, UT1, to Coordinated
22607		* Universal Time, UTC.
22608		*
22609		* <p>This function is derived from the International Astronomical Union's
22610		* SOFA (Standards of Fundamental Astronomy) software collection.
22611		*
22612		*<p>Status: canonical.
22613		*
22614		*<!-- Given: -->
22615		* @param ut11 double UT1 as a 2-part Julian Date (Note 1)
22616		* @param ut12 double UT1 as a 2-part Julian Date (Note 1)
22617		* dut1 double Delta UT1: UT1-UTC in seconds (Note 2)
22618		*
22619		*<!-- Returned:-->
22620		* @return JulianDate UTC as a 2-part quasi Julian Date (Notes 3,4)
22621		*
22622		* Returned (function value):
22623		* int status: +1 = dubious year (Note 5)
22624		* 0 = OK
22625		* -1 = unacceptable date
22626		*
22627		*<p>Notes:
22628		*<ol>
22629		* <li> ut11+ut12 is Julian Date, apportioned in any convenient way
22630		* between the two arguments, for example where ut11 is the Julian
22631		* Day Number and ut12 is the fraction of a day. The returned utc1
22632		* and utc2 form an analogous pair, except that a special convention
22633		* is used, to deal with the problem of leap seconds - see Note 3.
22634		*
22635		* <li> Delta UT1 can be obtained from tabulations provided by the
22636		* International Earth Rotation and Reference Systems Service. The
22637		* value changes abruptly by 1s at a leap second; however, close to
22638		* a leap second the algorithm used here is tolerant of the "wrong"
22639		* choice of value being made.
22640		*
22641		* <li> JD cannot unambiguously represent UTC during a leap second unless
22642		* special measures are taken. The convention in the present
22643		* function is that the returned quasi JD day UTC1+UTC2 represents
22644		* UTC days whether the length is 86399, 86400 or 86401 SI seconds.
22645		*
22646		* <li> The function jauD2dtf can be used to transform the UTC quasi-JD
22647		* into calendar date and clock time, including UTC leap second
22648		* handling.
22649		*
22650		* <li> The warning status "dubious year" flags UTCs that predate the
22651		* introduction of the time scale and that are too far in the future
22652		* to be trusted. See jauDat for further details.
22653		*</ol>
22654		* Called:
22655		* <ul>
22656		* <li>{@link #jauJd2cal} JD to Gregorian calendar
22657		* <li>{@link #jauDat} delta(AT) = TAI-UTC
22658		* <li>{@link #jauCal2jd} Gregorian calendar to JD
22659		*</ul>
22660		*<p>References:
22661		*
22662		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22663		* IERS Technical Note No. 32, BKG (2004)
22664		*
22665		* <p>Explanatory Supplement to the Astronomical Almanac,
22666		* P. Kenneth Seidelmann (ed), University Science Books (1992)
22667		*
22668		*@version 2010 May 16
22669		*
22670		*@since SOFA release 2010-12-01
22671		*
22672		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22673		* @throws JSOFAIllegalParameter
22674		* @throws JSOFAInternalError
22675		*/
22676		public static JulianDate jauUt1utc(double ut11, double ut12, double dut1) throws JSOFAIllegalParameter, JSOFAInternalError
22677
22678		{
22679
22680		double utc1, utc2;
22681		boolean big1;
22682		int i;
22683		double duts, u1, u2, d1, dats1, d2, fd, dats2, ddats, us1, us2, du;
22684
22685
22686		/* UT1-UTC in seconds. */
22687	2	duts = dut1;
22688
22689		/* Put the two parts of the UT1 into big-first order. */
22690	2	big1 = ( ut11 >= ut12 );
22691	2	if ( big1 ) {
22692	2	u1 = ut11;
22693	2	u2 = ut12;
22694		} else {
22695	0	u1 = ut12;
22696	0	u2 = ut11;
22697		}
22698
22699		/* See if the UT1 can possibly be in a leap-second day. */
22700	2	d1 = u1;
22701	2	dats1 = 0;
22702	12	for ( i = -1; i <= 3; i++ ) {
22703	10	d2 = u2 + (double) i;
22704	10	Calendar dt = jauJd2cal(d1, d2 );
22705	10	dats2 = jauDat(dt.iy, dt.im, dt.id, 0.0);
22706	10	if ( i == - 1 ) dats1 = dats2;
22707	10	ddats = dats2 - dats1;
22708	10	if ( abs(ddats) >= 0.5 ) {
22709
22710		/* Yes, leap second nearby: ensure UT1-UTC is "before" value. */
22711	0	if ( ddats * duts >= 0 ) duts -= ddats;
22712
22713		/* UT1 for the start of the UTC day that ends in a leap. */
22714	0	JulianDate jd = jauCal2jd(dt.iy, dt.im, dt.id );
22715	0	d1 = jd.djm0; d2 = jd.djm1;
22716	0	us1 = d1;
22717	0	us2 = d2 - 1.0 + duts/DAYSEC;
22718
22719		/* Is the UT1 after this point? */
22720	0	du = u1 - us1;
22721	0	du += u2 - us2;
22722	0	if ( du > 0 ) {
22723
22724		/* Yes: fraction of the current UTC day that has elapsed. */
22725	0	fd = du * DAYSEC / ( DAYSEC + ddats );
22726
22727		/* Ramp UT1-UTC to bring about SOFA's JD(UTC) convention. */
22728	0	duts += ddats * ( fd <= 1.0 ? fd : 1.0 );
22729		}
22730
22731		/* Done. */
22732		break;
22733		}
22734	10	dats1 = dats2;
22735		}
22736
22737		/* Subtract the (possibly adjusted) UT1-UTC from UT1 to give UTC. */
22738	2	u2 -= duts / DAYSEC;
22739
22740		/* Result, safeguarding precision. */
22741	2	if ( big1 ) {
22742	2	utc1 = u1;
22743	2	utc2 = u2;
22744		} else {
22745	0	utc1 = u2;
22746	0	utc2 = u1;
22747		}
22748
22749		/* FIXME Status. */
22750	2	return new JulianDate(utc1, utc2);
22751
22752		};
22753
22754		/**
22755		*
22756		* Time scale transformation: Coordinated Universal Time, UTC, to
22757		* International Atomic Time, TAI.
22758		*
22759		* <p>This function is derived from the International Astronomical Union's
22760		* SOFA (Standards of Fundamental Astronomy) software collection.
22761		*
22762		*<p>Status: canonical.
22763		*
22764		*<!-- Given: -->
22765		* @param utc1 double UTC as a 2-part quasi Julian Date (Notes 1-4)
22766		* @param utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4)
22767		*
22768		*<!-- Returned:-->
22769		* @return JulianDate TAI as a 2-part Julian Date (Note 5)
22770		*
22771		* Returned (function value):
22772		* int status: +1 = dubious year (Note 3)
22773		* 0 = OK
22774		* -1 = unacceptable date
22775		*
22776		*<p>Notes:
22777		*<ol>
22778		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
22779		* convenient way between the two arguments, for example where utc1
22780		* is the Julian Day Number and utc2 is the fraction of a day.
22781		*
22782		* <li> JD cannot unambiguously represent UTC during a leap second unless
22783		* special measures are taken. The convention in the present
22784		* function is that the JD day represents UTC days whether the
22785		* length is 86399, 86400 or 86401 SI seconds.
22786		*
22787		* <li> The warning status "dubious year" flags UTCs that predate the
22788		* introduction of the time scale and that are too far in the future
22789		* to be trusted. See jauDat for further details.
22790		*
22791		* <li> The function jauDtf2d converts from calendar date and time of day
22792		* into 2-part Julian Date, and in the case of UTC implements the
22793		* leap-second-ambiguity convention described above.
22794		*
22795		* <li> The returned TAI1,TAI2 are such that their sum is the TAI Julian
22796		* Date.
22797		*</ol>
22798		* Called:<ul>
22799		* <li>{@link #jauJd2cal} JD to Gregorian calendar
22800		* <li>{@link #jauDat} delta(AT) = TAI-UTC
22801		* <li>{@link #jauCal2jd} Gregorian calendar to JD
22802		*</ul>
22803		*<p>References:
22804		*
22805		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22806		* IERS Technical Note No. 32, BKG (2004)
22807		*
22808		* Explanatory Supplement to the Astronomical Almanac,
22809		* P. Kenneth Seidelmann (ed), University Science Books (1992)
22810		*
22811		*@version 2010 September 10
22812		*
22813		*@since SOFA release 2010-12-01
22814		*
22815		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22816		* @throws JSOFAInternalError
22817		* @throws JSOFAIllegalParameter
22818		*
22819		*/
22820		public static JulianDate jauUtctai(double utc1, double utc2) throws JSOFAIllegalParameter, JSOFAInternalError
22821
22822		{
22823		double tai1, tai2;
22824		boolean big1;
22825		double u1, u2, dats, datst, ddat, a2, fd;
22826
22827
22828		/* Put the two parts of the UTC into big-first order. */
22829	52	big1 = ( utc1 >= utc2 );
22830	52	if ( big1 ) {
22831	52	u1 = utc1;
22832	52	u2 = utc2;
22833		} else {
22834	0	u1 = utc2;
22835	0	u2 = utc1;
22836		}
22837
22838		/* Get TAI-UTC now. */
22839	52	Calendar dt = jauJd2cal(u1, u2 );
22840	52	dats = jauDat(dt.iy, dt.im, dt.id, dt.fd);
22841		// if ( js < 0 ) return -1;
22842	52	fd = dt.fd;
22843		/* Get TAI-UTC tomorrow. */
22844	52	Calendar dtt = jauJd2cal(u1+1.5, u2-fd );
22845	52	datst = jauDat(dtt.iy, dtt.im, dtt.id, dtt.fd);
22846		// if ( js < 0 ) return -1;
22847
22848		/* If today ends in a leap second, scale the fraction into SI days. */
22849	52	ddat = datst - dats;
22850	52	if ( abs(ddat) > 0.5 ) fd += fd * ddat / DAYSEC;
22851
22852		/* Today's calendar date to 2-part JD. */
22853	52	JulianDate jd = jauCal2jd(dt.iy, dt.im, dt.id ) ;
22854
22855		/* Assemble the TAI result, preserving the UTC split and order. */
22856	52	a2 = jd.djm0 - u1;
22857	52	a2 += jd.djm1;
22858	52	a2 += fd + dats / DAYSEC;
22859	52	if ( big1 ) {
22860	52	tai1 = u1;
22861	52	tai2 = a2;
22862		} else {
22863	0	tai1 = a2;
22864	0	tai2 = u1;
22865		}
22866
22867		/* FIXME Status. */
22868	52	return new JulianDate(tai1, tai2);
22869
22870		};
22871
22872		/**
22873		*
22874		* Time scale transformation: Coordinated Universal Time, UTC, to
22875		* Universal Time, UT1.
22876		*
22877		* <p>This function is derived from the International Astronomical Union's
22878		* SOFA (Standards of Fundamental Astronomy) software collection.
22879		*
22880		*<p>Status: canonical.
22881		*
22882		*<!-- Given: -->
22883		* utc1,utc2 double UTC as a 2-part quasi Julian Date (Notes 1-4)
22884		* dut1 double Delta UT1 = UT1-UTC in seconds (Note 5)
22885		*
22886		*<!-- Returned:-->
22887		* ut11,ut12 double UT1 as a 2-part Julian Date (Note 6)
22888		*
22889		* Returned (function value):
22890		* int status: +1 = dubious year (Note 7)
22891		* 0 = OK
22892		* -1 = unacceptable date
22893		*
22894		*<p>Notes:
22895		*<ol>
22896		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
22897		* convenient way between the two arguments, for example where utc1
22898		* is the Julian Day Number and utc2 is the fraction of a day.
22899		*
22900		* <li> JD cannot unambiguously represent UTC during a leap second unless
22901		* special measures are taken. The convention in the present
22902		* function is that the JD day represents UTC days whether the
22903		* length is 86399, 86400 or 86401 SI seconds.
22904		*
22905		* <li> The warning status "dubious year" flags UTCs that predate the
22906		* introduction of the time scale and that are too far in the future
22907		* to be trusted. See jauDat for further details.
22908		*
22909		* <li> The function jauDtf2d converts from calendar date and time of
22910		* day into 2-part Julian Date, and in the case of UTC implements
22911		* the leap-second-ambiguity convention described above.
22912		*
22913		* <li> Delta UT1 can be obtained from tabulations provided by the
22914		* International Earth Rotation and Reference Systems Service. It
22915		* It is the caller's responsibility to supply a DUT argument
22916		* containing the UT1-UTC value that matches the given UTC.
22917		*
22918		* <li> The returned ut11,ut12 are such that their sum is the UT1 Julian
22919		* Date.
22920		*
22921		* <li> The warning status "dubious year" flags UTCs that predate the
22922		* introduction of the time scale and that are too far in the future
22923		* to be trusted. See jauDat for further details.
22924		*</ol>
22925		*<p>References:
22926		*
22927		* McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
22928		* IERS Technical Note No. 32, BKG (2004)
22929		*
22930		* Explanatory Supplement to the Astronomical Almanac,
22931		* P. Kenneth Seidelmann (ed), University Science Books (1992)
22932		*
22933		* Called:<ul>
22934		* <li>{@link #jauJd2cal} JD to Gregorian calendar
22935		* <li>{@link #jauDat} delta(AT) = TAI-UTC
22936		* <li>{@link #jauUtctai} UTC to TAI
22937		* <li>{@link #jauTaiut1} TAI to UT1
22938		*</ul>
22939		*@version 2010 May 16
22940		*
22941		*@since SOFA release 2010-12-01
22942		*
22943		* <!-- Copyright (C) 2010 IAU SOFA Board. See notes at end. -->
22944		* @throws JSOFAInternalError
22945		* @throws JSOFAIllegalParameter
22946		*/
22947		public static JulianDate jauUtcut1(double utc1, double utc2, double dut1) throws JSOFAIllegalParameter, JSOFAInternalError
22948		{
22949
22950
22951		double dta;
22952		/* Look up TAI-UTC. */
22953	26	Calendar dt = jauJd2cal(utc1, utc2) ;
22954	26	double dat = jauDat ( dt.iy, dt.im, dt.id, 0.0 );
22955
22956
22957		/* Form UT1-TAI. */
22958	26	dta = dut1 - dat;
22959
22960		/* UTC to TAI to UT1. */
22961	26	JulianDate tai = jauUtctai(utc1, utc2);
22962	26	return jauTaiut1(tai.djm0, tai.djm1, dta) ;
22963
22964		};
22965
22966
22967		public static CelestialIntermediatePole jauXy06(double date1, double date2)
22968		/**
22969		* X,Y coordinates of celestial intermediate pole from series based
22970		* on IAU 2006 precession and IAU 2000A nutation.
22971		*
22972		*<p>This function is derived from the International Astronomical Union's
22973		* SOFA (Standards Of Fundamental Astronomy) software collection.
22974		*
22975		*<p>Status: canonical model.
22976		*
22977		*<!-- Given: -->
22978		* @param date1 double TT as a 2-part Julian Date (Note 1)
22979		* @param date2 double TT as a 2-part Julian Date (Note 1)
22980		*
22981		*<!-- Returned: -->
22982		* @return CIP X,Y coordinates (Note 2)
22983		*
22984		* <p>Notes:
22985		* <ol>
22986		*
22987		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
22988		* convenient way between the two arguments. For example,
22989		* JD(TT)=2450123.7 could be expressed in any of these ways,
22990		* among others:
22991		*<pre>
22992		* date1 date2
22993		*
22994		* 2450123.7 0.0 (JD method)
22995		* 2451545.0 -1421.3 (J2000 method)
22996		* 2400000.5 50123.2 (MJD method)
22997		* 2450123.5 0.2 (date & time method)
22998		*</pre>
22999		* The JD method is the most natural and convenient to use in
23000		* cases where the loss of several decimal digits of resolution
23001		* is acceptable. The J2000 method is best matched to the way
23002		* the argument is handled internally and will deliver the
23003		* optimum resolution. The MJD method and the date & time methods
23004		* are both good compromises between resolution and convenience.
23005		*
23006		* <li> The X,Y coordinates are those of the unit vector towards the
23007		* celestial intermediate pole. They represent the combined effects
23008		* of frame bias, precession and nutation.
23009		*
23010		* <li> The fundamental arguments used are as adopted in IERS Conventions
23011		* (2003) and are from Simon et al. (1994) and Souchay et al.
23012		* (1999).
23013		*
23014		* <li> This is an alternative to the angles-based method, via the JSOFA
23015		* function jauFw2xy and as used in jauXys06a for example. The two
23016		* methods agree at the 1 microarcsecond level (at present), a
23017		* negligible amount compared with the intrinsic accuracy of the
23018		* models. However, it would be unwise to mix the two methods
23019		* (angles-based and series-based) in a single application.
23020		*</ol>
23021		*<p>Called:<ul>
23022		* <li>{@link #jauFal03} mean anomaly of the Moon
23023		* <li>{@link #jauFalp03} mean anomaly of the Sun
23024		* <li>{@link #jauFaf03} mean argument of the latitude of the Moon
23025		* <li>{@link #jauFad03} mean elongation of the Moon from the Sun
23026		* <li>{@link #jauFaom03} mean longitude of the Moon's ascending node
23027		* <li>{@link #jauFame03} mean longitude of Mercury
23028		* <li>{@link #jauFave03} mean longitude of Venus
23029		* <li>{@link #jauFae03} mean longitude of Earth
23030		* <li>{@link #jauFama03} mean longitude of Mars
23031		* <li>{@link #jauFaju03} mean longitude of Jupiter
23032		* <li>{@link #jauFasa03} mean longitude of Saturn
23033		* <li>{@link #jauFaur03} mean longitude of Uranus
23034		* <li>{@link #jauFane03} mean longitude of Neptune
23035		* <li>{@link #jauFapa03} general accumulated precession in longitude
23036		* </ul>
23037		*<p>References:
23038		*
23039		* <p>Capitaine, N., Wallace, P.T. & Chapront, J., 2003,
23040		* Astron.Astrophys., 412, 567
23041		*
23042		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
23043		*
23044		* <p>McCarthy, D. D., Petit, G. (eds.), 2004, IERS Conventions (2003),
23045		* IERS Technical Note No. 32, BKG
23046		*
23047		* Simon, J.L., Bretagnon, P., Chapront, J., Chapront-Touze, M.,
23048		* Francou, G. & Laskar, J., Astron.Astrophys., 1994, 282, 663
23049		*
23050		* Souchay, J., Loysel, B., Kinoshita, H., Folgueira, M., 1999,
23051		* Astron.Astrophys.Supp.Ser. 135, 111
23052		*
23053		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
23054		*
23055		*@version 2009 October 16
23056		*
23057		* @since Release 20101201
23058		*
23059		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
23060		*/
23061		{
23062
23063		/* Maximum power of T in the polynomials for X and Y */
23064	2	final int MAXPT = (5);
23065
23066		/* Polynomial coefficients (arcsec, X then Y). */
23067	2	final double xyp[][] = {
23068
23069		{ -0.016617,
23070		2004.191898,
23071		-0.4297829,
23072		-0.19861834,
23073		0.000007578,
23074		0.0000059285
23075		},
23076		{ -0.006951,
23077		-0.025896,
23078		-22.4072747,
23079		0.00190059,
23080		0.001112526,
23081		0.0000001358
23082		}
23083		};
23084
23085		/* N.B mfals defined as class static (outside this method) to avoid problems with 65535 byte limit for methods */
23086		/* Number of frequencies: luni-solar */
23087	2	final int NFLS = mfals.length;
23088
23089		/* Number of frequencies: planetary */
23090	2	final int NFPL =mfapl.length ;
23091
23092		/* Pointers into amplitudes array, one pointer per frequency */
23093	2	final int nc[] = {
23094
23095		/* 1-100 */
23096		1, 21, 37, 51, 65, 79, 91, 103, 115, 127,
23097		139, 151, 163, 172, 184, 196, 207, 219, 231, 240,
23098		252, 261, 273, 285, 297, 309, 318, 327, 339, 351,
23099		363, 372, 384, 396, 405, 415, 423, 435, 444, 452,
23100		460, 467, 474, 482, 490, 498, 506, 513, 521, 528,
23101		536, 543, 551, 559, 566, 574, 582, 590, 597, 605,
23102		613, 620, 628, 636, 644, 651, 658, 666, 674, 680,
23103		687, 695, 702, 710, 717, 725, 732, 739, 746, 753,
23104		760, 767, 774, 782, 790, 798, 805, 812, 819, 826,
23105		833, 840, 846, 853, 860, 867, 874, 881, 888, 895,
23106
23107		/* 101-200 */
23108		901, 908, 914, 921, 928, 934, 941, 948, 955, 962,
23109		969, 976, 982, 989, 996, 1003, 1010, 1017, 1024, 1031,
23110		1037, 1043, 1050, 1057, 1064, 1071, 1078, 1084, 1091, 1098,
23111		1104, 1112, 1118, 1124, 1131, 1138, 1145, 1151, 1157, 1164,
23112		1171, 1178, 1185, 1192, 1199, 1205, 1212, 1218, 1226, 1232,
23113		1239, 1245, 1252, 1259, 1266, 1272, 1278, 1284, 1292, 1298,
23114		1304, 1310, 1316, 1323, 1329, 1335, 1341, 1347, 1353, 1359,
23115		1365, 1371, 1377, 1383, 1389, 1396, 1402, 1408, 1414, 1420,
23116		1426, 1434, 1440, 1446, 1452, 1459, 1465, 1471, 1477, 1482,
23117		1488, 1493, 1499, 1504, 1509, 1514, 1520, 1527, 1532, 1538,
23118
23119		/* 201-300 */
23120		1543, 1548, 1553, 1558, 1564, 1569, 1574, 1579, 1584, 1589,
23121		1594, 1596, 1598, 1600, 1602, 1605, 1608, 1610, 1612, 1617,
23122		1619, 1623, 1625, 1627, 1629, 1632, 1634, 1640, 1642, 1644,
23123		1646, 1648, 1650, 1652, 1654, 1658, 1660, 1662, 1664, 1668,
23124		1670, 1672, 1673, 1675, 1679, 1681, 1683, 1684, 1686, 1688,
23125		1690, 1693, 1695, 1697, 1701, 1703, 1705, 1707, 1709, 1711,
23126		1712, 1715, 1717, 1721, 1723, 1725, 1727, 1729, 1731, 1733,
23127		1735, 1737, 1739, 1741, 1743, 1745, 1747, 1749, 1751, 1753,
23128		1755, 1757, 1759, 1761, 1762, 1764, 1766, 1768, 1769, 1771,
23129		1773, 1775, 1777, 1779, 1781, 1783, 1785, 1787, 1788, 1790,
23130
23131		/* 301-400 */
23132		1792, 1794, 1796, 1798, 1800, 1802, 1804, 1806, 1807, 1809,
23133		1811, 1815, 1817, 1819, 1821, 1823, 1825, 1827, 1829, 1831,
23134		1833, 1835, 1837, 1839, 1840, 1842, 1844, 1848, 1850, 1852,
23135		1854, 1856, 1858, 1859, 1860, 1862, 1864, 1866, 1868, 1869,
23136		1871, 1873, 1875, 1877, 1879, 1881, 1883, 1885, 1887, 1889,
23137		1891, 1892, 1896, 1898, 1900, 1901, 1903, 1905, 1907, 1909,
23138		1910, 1911, 1913, 1915, 1919, 1921, 1923, 1927, 1929, 1931,
23139		1933, 1935, 1937, 1939, 1943, 1945, 1947, 1948, 1949, 1951,
23140		1953, 1955, 1957, 1958, 1960, 1962, 1964, 1966, 1968, 1970,
23141		1971, 1973, 1974, 1975, 1977, 1979, 1980, 1981, 1982, 1984,
23142
23143		/* 401-500 */
23144		1986, 1988, 1990, 1992, 1994, 1995, 1997, 1999, 2001, 2003,
23145		2005, 2007, 2008, 2009, 2011, 2013, 2015, 2017, 2019, 2021,
23146		2023, 2024, 2025, 2027, 2029, 2031, 2033, 2035, 2037, 2041,
23147		2043, 2045, 2046, 2047, 2049, 2051, 2053, 2055, 2056, 2057,
23148		2059, 2061, 2063, 2065, 2067, 2069, 2070, 2071, 2072, 2074,
23149		2076, 2078, 2080, 2082, 2084, 2086, 2088, 2090, 2092, 2094,
23150		2095, 2096, 2097, 2099, 2101, 2105, 2106, 2107, 2108, 2109,
23151		2110, 2111, 2113, 2115, 2119, 2121, 2123, 2125, 2127, 2129,
23152		2131, 2133, 2135, 2136, 2137, 2139, 2141, 2143, 2145, 2147,
23153		2149, 2151, 2153, 2155, 2157, 2159, 2161, 2163, 2165, 2167,
23154
23155		/* 501-600 */
23156		2169, 2171, 2173, 2175, 2177, 2179, 2181, 2183, 2185, 2186,
23157		2187, 2188, 2192, 2193, 2195, 2197, 2199, 2201, 2203, 2205,
23158		2207, 2209, 2211, 2213, 2217, 2219, 2221, 2223, 2225, 2227,
23159		2229, 2231, 2233, 2234, 2235, 2236, 2237, 2238, 2239, 2240,
23160		2241, 2244, 2246, 2248, 2250, 2252, 2254, 2256, 2258, 2260,
23161		2262, 2264, 2266, 2268, 2270, 2272, 2274, 2276, 2278, 2280,
23162		2282, 2284, 2286, 2288, 2290, 2292, 2294, 2296, 2298, 2300,
23163		2302, 2303, 2304, 2305, 2306, 2307, 2309, 2311, 2313, 2315,
23164		2317, 2319, 2321, 2323, 2325, 2327, 2329, 2331, 2333, 2335,
23165		2337, 2341, 2343, 2345, 2347, 2349, 2351, 2352, 2355, 2356,
23166
23167		/* 601-700 */
23168		2357, 2358, 2359, 2361, 2363, 2364, 2365, 2366, 2367, 2368,
23169		2369, 2370, 2371, 2372, 2373, 2374, 2376, 2378, 2380, 2382,
23170		2384, 2385, 2386, 2387, 2388, 2389, 2390, 2391, 2392, 2393,
23171		2394, 2395, 2396, 2397, 2398, 2399, 2400, 2401, 2402, 2403,
23172		2404, 2405, 2406, 2407, 2408, 2409, 2410, 2411, 2412, 2413,
23173		2414, 2415, 2417, 2418, 2430, 2438, 2445, 2453, 2460, 2468,
23174		2474, 2480, 2488, 2496, 2504, 2512, 2520, 2527, 2535, 2543,
23175		2550, 2558, 2566, 2574, 2580, 2588, 2596, 2604, 2612, 2619,
23176		2627, 2634, 2642, 2648, 2656, 2664, 2671, 2679, 2685, 2693,
23177		2701, 2709, 2717, 2725, 2733, 2739, 2747, 2753, 2761, 2769,
23178
23179		/* 701-800 */
23180		2777, 2785, 2793, 2801, 2809, 2817, 2825, 2833, 2841, 2848,
23181		2856, 2864, 2872, 2878, 2884, 2892, 2898, 2906, 2914, 2922,
23182		2930, 2938, 2944, 2952, 2958, 2966, 2974, 2982, 2988, 2996,
23183		3001, 3009, 3017, 3025, 3032, 3039, 3045, 3052, 3059, 3067,
23184		3069, 3076, 3083, 3090, 3098, 3105, 3109, 3111, 3113, 3120,
23185		3124, 3128, 3132, 3136, 3140, 3144, 3146, 3150, 3158, 3161,
23186		3165, 3166, 3168, 3172, 3176, 3180, 3182, 3185, 3189, 3193,
23187		3194, 3197, 3200, 3204, 3208, 3212, 3216, 3219, 3221, 3222,
23188		3226, 3230, 3234, 3238, 3242, 3243, 3247, 3251, 3254, 3258,
23189		3262, 3266, 3270, 3274, 3275, 3279, 3283, 3287, 3289, 3293,
23190
23191		/* 801-900 */
23192		3296, 3300, 3303, 3307, 3311, 3315, 3319, 3321, 3324, 3327,
23193		3330, 3334, 3338, 3340, 3342, 3346, 3350, 3354, 3358, 3361,
23194		3365, 3369, 3373, 3377, 3381, 3385, 3389, 3393, 3394, 3398,
23195		3402, 3406, 3410, 3413, 3417, 3421, 3425, 3429, 3433, 3435,
23196		3439, 3443, 3446, 3450, 3453, 3457, 3458, 3461, 3464, 3468,
23197		3472, 3476, 3478, 3481, 3485, 3489, 3493, 3497, 3501, 3505,
23198		3507, 3511, 3514, 3517, 3521, 3524, 3525, 3527, 3529, 3533,
23199		3536, 3540, 3541, 3545, 3548, 3551, 3555, 3559, 3563, 3567,
23200		3569, 3570, 3574, 3576, 3578, 3582, 3586, 3590, 3593, 3596,
23201		3600, 3604, 3608, 3612, 3616, 3620, 3623, 3626, 3630, 3632,
23202
23203		/* 901-1000 */
23204		3636, 3640, 3643, 3646, 3648, 3652, 3656, 3660, 3664, 3667,
23205		3669, 3671, 3675, 3679, 3683, 3687, 3689, 3693, 3694, 3695,
23206		3699, 3703, 3705, 3707, 3710, 3713, 3717, 3721, 3725, 3729,
23207		3733, 3736, 3740, 3744, 3748, 3752, 3754, 3757, 3759, 3763,
23208		3767, 3770, 3773, 3777, 3779, 3783, 3786, 3790, 3794, 3798,
23209		3801, 3805, 3809, 3813, 3817, 3821, 3825, 3827, 3831, 3835,
23210		3836, 3837, 3840, 3844, 3848, 3852, 3856, 3859, 3863, 3867,
23211		3869, 3871, 3875, 3879, 3883, 3887, 3890, 3894, 3898, 3901,
23212		3905, 3909, 3913, 3917, 3921, 3922, 3923, 3924, 3926, 3930,
23213		3932, 3936, 3938, 3940, 3944, 3948, 3952, 3956, 3959, 3963,
23214
23215		/* 1001-1100 */
23216		3965, 3969, 3973, 3977, 3979, 3981, 3982, 3986, 3989, 3993,
23217		3997, 4001, 4004, 4006, 4009, 4012, 4016, 4020, 4024, 4026,
23218		4028, 4032, 4036, 4040, 4044, 4046, 4050, 4054, 4058, 4060,
23219		4062, 4063, 4064, 4068, 4071, 4075, 4077, 4081, 4083, 4087,
23220		4089, 4091, 4095, 4099, 4101, 4103, 4105, 4107, 4111, 4115,
23221		4119, 4123, 4127, 4129, 4131, 4135, 4139, 4141, 4143, 4145,
23222		4149, 4153, 4157, 4161, 4165, 4169, 4173, 4177, 4180, 4183,
23223		4187, 4191, 4195, 4198, 4201, 4205, 4209, 4212, 4213, 4216,
23224		4217, 4221, 4223, 4226, 4230, 4234, 4236, 4240, 4244, 4248,
23225		4252, 4256, 4258, 4262, 4264, 4266, 4268, 4270, 4272, 4276,
23226
23227		/* 1101-1200 */
23228		4279, 4283, 4285, 4287, 4289, 4293, 4295, 4299, 4300, 4301,
23229		4305, 4309, 4313, 4317, 4319, 4323, 4325, 4329, 4331, 4333,
23230		4335, 4337, 4341, 4345, 4349, 4351, 4353, 4357, 4361, 4365,
23231		4367, 4369, 4373, 4377, 4381, 4383, 4387, 4389, 4391, 4395,
23232		4399, 4403, 4407, 4411, 4413, 4414, 4415, 4418, 4419, 4421,
23233		4423, 4427, 4429, 4431, 4433, 4435, 4437, 4439, 4443, 4446,
23234		4450, 4452, 4456, 4458, 4460, 4462, 4466, 4469, 4473, 4477,
23235		4481, 4483, 4487, 4489, 4491, 4493, 4497, 4499, 4501, 4504,
23236		4506, 4510, 4513, 4514, 4515, 4518, 4521, 4522, 4525, 4526,
23237		4527, 4530, 4533, 4534, 4537, 4541, 4542, 4543, 4544, 4545,
23238
23239		/* 1201-1300 */
23240		4546, 4547, 4550, 4553, 4554, 4555, 4558, 4561, 4564, 4567,
23241		4568, 4571, 4574, 4575, 4578, 4581, 4582, 4585, 4586, 4588,
23242		4590, 4592, 4596, 4598, 4602, 4604, 4608, 4612, 4613, 4616,
23243		4619, 4622, 4623, 4624, 4625, 4626, 4629, 4632, 4633, 4636,
23244		4639, 4640, 4641, 4642, 4643, 4644, 4645, 4648, 4649, 4650,
23245		4651, 4652, 4653, 4656, 4657, 4660, 4661, 4664, 4667, 4670,
23246		4671, 4674, 4675, 4676, 4677, 4678, 4681, 4682, 4683, 4684,
23247		4687, 4688, 4689, 4692, 4693, 4696, 4697, 4700, 4701, 4702,
23248		4703, 4704, 4707, 4708, 4711, 4712, 4715, 4716, 4717, 4718,
23249		4719, 4720, 4721, 4722, 4723, 4726, 4729, 4730, 4733, 4736,
23250
23251		/* 1301-(NFLS+NFPL) */
23252		4737, 4740, 4741, 4742, 4745, 4746, 4749, 4752, 4753
23253		};
23254
23255		/* Amplitude coefficients (microarcsec); indexed using the nc array. */
23256	2	final double a[] = {
23257
23258		/* 1-105 */
23259		-6844318.44, 9205236.26,1328.67,1538.18, 205833.11,
23260		153041.79, -3309.73, 853.32,2037.98, -2301.27,
23261		81.46, 120.56, -20.39, -15.22, 1.73, -1.61, -0.10, 0.11,
23262		-0.02, -0.02, -523908.04, 573033.42,-544.75,-458.66,
23263		12814.01, 11714.49, 198.97,-290.91, 155.74,-143.27,
23264		-2.75, -1.03, -1.27, -1.16, 0.00, -0.01, -90552.22,
23265		97846.69, 111.23, 137.41,2187.91,2024.68, 41.44, -51.26,
23266		26.92, -24.46, -0.46, -0.28, -0.22, -0.20, 82168.76,
23267		-89618.24, -27.64, -29.05, -2004.36, -1837.32,
23268		-36.07, 48.00, -24.43, 22.41, 0.47, 0.24, 0.20, 0.18,
23269		58707.02,7387.02, 470.05,-192.40, 164.33, -1312.21,
23270		-179.73, -28.93, -17.36, -1.83, -0.50, 3.57, 0.00, 0.13,
23271		-20557.78, 22438.42, -20.84, -17.40, 501.82, 459.68,
23272		59.20, -67.30, 6.08, -5.61, -1.36, -1.19, 28288.28,
23273		-674.99, -34.69, 35.80, -15.07,-632.54, -11.19, 0.78, -8.41,
23274		0.17, 0.01, 0.07, -15406.85, 20069.50, 15.12,
23275
23276		/* 106-219 */
23277		31.80, 448.76, 344.50, -5.77, 1.41, 4.59, -5.02, 0.17,
23278		0.24, -11991.74, 12902.66, 32.46, 36.70, 288.49,
23279		268.14, 5.70, -7.06, 3.57, -3.23, -0.06, -0.04,
23280		-8584.95, -9592.72, 4.42, -13.20,-214.50, 192.06,
23281		23.87, 29.83, 2.54, 2.40, 0.60, -0.48,5095.50,
23282		-6918.22, 7.19, 3.92,-154.91,-113.94, 2.86, -1.04,
23283		-1.52, 1.73, -0.07, -0.10, -4910.93, -5331.13,
23284		0.76, 0.40,-119.21, 109.81, 2.16, 3.20, 1.46, 1.33,
23285		0.04, -0.02, -6245.02,-123.48, -6.68, -8.20, -2.76,
23286		139.64, 2.71, 0.15, 1.86,2511.85, -3323.89, 1.07,
23287		-0.90, -74.33, -56.17, 1.16, -0.01, -0.75, 0.83, -0.02,
23288		-0.04,2307.58,3143.98, -7.52, 7.50, 70.31, -51.60, 1.46,
23289		0.16, -0.69, -0.79, 0.02, -0.05,2372.58,2554.51, 5.93,
23290		-6.60, 57.12, -53.05, -0.96, -1.24, -0.71, -0.64, -0.01,
23291		-2053.16,2636.13, 5.13, 7.80, 58.94, 45.91, -0.42,
23292		-0.12, 0.61, -0.66, 0.02, 0.03, -1825.49,
23293
23294		/* 220-339 */
23295		-2423.59, 1.23, -2.00, -54.19, 40.82, -1.07, -1.02,
23296		0.54, 0.61, -0.04, 0.04,2521.07,-122.28, -5.97, 2.90,
23297		-2.73, -56.37, -0.82, 0.13, -0.75, -1534.09,1645.01,
23298		6.29, 6.80, 36.78, 34.30, 0.92, -1.25, 0.46, -0.41,
23299		-0.02, -0.01,1898.27, 47.70, -0.72, 2.50, 1.07, -42.45,
23300		-0.94, 0.02, -0.56, -1292.02, -1387.00, 0.00,
23301		0.00, -31.01, 28.89, 0.68, 0.00, 0.38, 0.35, -0.01,
23302		-0.01, -1234.96,1323.81, 5.21, 5.90, 29.60, 27.61,
23303		0.74, -1.22, 0.37, -0.33, -0.02, -0.01,1137.48,
23304		-1233.89, -0.04, -0.30, -27.59, -25.43, -0.61, 1.00,
23305		-0.34, 0.31, 0.01, 0.01,-813.13, -1075.60, 0.40,
23306		0.30, -24.05, 18.18, -0.40, -0.01, 0.24, 0.27, -0.01,
23307		0.01,1163.22, -60.90, -2.94, 1.30, -1.36, -26.01, -0.58,
23308		0.07, -0.35,1029.70, -55.55, -2.63, 1.10, -1.25, -23.02,
23309		-0.52, 0.06, -0.31,-556.26, 852.85, 3.16, -4.48, 19.06,
23310		12.44, -0.81, -0.27, 0.17, -0.21, 0.00, 0.02,-603.52,
23311
23312		/* 340-467 */
23313		-800.34, 0.44, 0.10, -17.90, 13.49, -0.08, -0.01, 0.18,
23314		0.20, -0.01, 0.01,-628.24, 684.99, -0.64, -0.50, 15.32,
23315		14.05, 3.18, -4.19, 0.19, -0.17, -0.09, -0.07,-866.48,
23316		-16.26, 0.52, -1.30, -0.36, 19.37, 0.43, -0.01, 0.26,
23317		-512.37, 695.54, -1.47, -1.40, 15.55, 11.46, -0.16, 0.03,
23318		0.15, -0.17, 0.01, 0.01, 506.65, 643.75, 2.54, -2.62,
23319		14.40, -11.33, -0.77, -0.06, -0.15, -0.16, 0.00, 0.01,
23320		664.57, 16.81, -0.40, 1.00, 0.38, -14.86, -3.71, -0.09,
23321		-0.20, 405.91, 522.11, 0.99, -1.50, 11.67, -9.08, -0.25,
23322		-0.02, -0.12, -0.13,-305.78, 326.60, 1.75, 1.90, 7.30,
23323		6.84, 0.20, -0.04, 300.99,-325.03, -0.44, -0.50, -7.27,
23324		-6.73, -1.01, 0.01, 0.00, 0.08, 0.00, 0.02, 438.51,
23325		10.47, -0.56, -0.20, 0.24, -9.81, -0.24, 0.01, -0.13,
23326		-264.02, 335.24, 0.99, 1.40, 7.49, 5.90, -0.27, -0.02,
23327		284.09, 307.03, 0.32, -0.40, 6.87, -6.35, -0.99, -0.01,
23328		-250.54, 327.11, 0.08, 0.40, 7.31, 5.60, -0.30, 230.72,
23329
23330		/* 468-595 */
23331		-304.46, 0.08, -0.10, -6.81, -5.16, 0.27, 229.78, 304.17,
23332		-0.60, 0.50, 6.80, -5.14, 0.33, 0.01, 256.30,-276.81,
23333		-0.28, -0.40, -6.19, -5.73, -0.14, 0.01,-212.82, 269.45,
23334		0.84, 1.20, 6.02, 4.76, 0.14, -0.02, 196.64, 272.05,
23335		-0.84, 0.90, 6.08, -4.40, 0.35, 0.02, 188.95, 272.22,
23336		-0.12, 0.30, 6.09, -4.22, 0.34,-292.37, -5.10, -0.32,
23337		-0.40, -0.11, 6.54, 0.14, 0.01, 161.79,-220.67, 0.24,
23338		0.10, -4.93, -3.62, -0.08, 261.54, -19.94, -0.95, 0.20,
23339		-0.45, -5.85, -0.13, 0.02, 142.16,-190.79, 0.20, 0.10,
23340		-4.27, -3.18, -0.07, 187.95, -4.11, -0.24, 0.30, -0.09,
23341		-4.20, -0.09, 0.01, 0.00, 0.00, -79.08, 167.90, 0.04,
23342		0.00, 3.75, 1.77, 121.98, 131.04, -0.08, 0.10, 2.93,
23343		-2.73, -0.06,-172.95, -8.11, -0.40, -0.20, -0.18, 3.87,
23344		0.09, 0.01,-160.15, -55.30, -14.04, 13.90, -1.23, 3.58,
23345		0.40, 0.31,-115.40, 123.20, 0.60, 0.70, 2.75, 2.58,
23346		0.08, -0.01,-168.26, -2.00, 0.20, -0.20, -0.04, 3.76,
23347
23348		/* 596-723 */
23349		0.08,-114.49, 123.20, 0.32, 0.40, 2.75, 2.56, 0.07,
23350		-0.01, 112.14, 120.70, 0.28, -0.30, 2.70, -2.51, -0.07,
23351		-0.01, 161.34, 4.03, 0.20, 0.20, 0.09, -3.61, -0.08,
23352		91.31, 126.64, -0.40, 0.40, 2.83, -2.04, -0.04, 0.01,
23353		105.29, 112.90, 0.44, -0.50, 2.52, -2.35, -0.07, -0.01,
23354		98.69,-106.20, -0.28, -0.30, -2.37, -2.21, -0.06, 0.01,
23355		86.74,-112.94, -0.08, -0.20, -2.53, -1.94, -0.05,-134.81,
23356		3.51, 0.20, -0.20, 0.08, 3.01, 0.07, 79.03, 107.31,
23357		-0.24, 0.20, 2.40, -1.77, -0.04, 0.01, 132.81, -10.77,
23358		-0.52, 0.10, -0.24, -2.97, -0.07, 0.01,-130.31, -0.90,
23359		0.04, 0.00, 0.00, 2.91, -78.56, 85.32, 0.00, 0.00,
23360		1.91, 1.76, 0.04, 0.00, 0.00, -41.53, 89.10, 0.02,
23361		0.00, 1.99, 0.93, 66.03, -71.00, -0.20, -0.20, -1.59,
23362		-1.48, -0.04, 60.50, 64.70, 0.36, -0.40, 1.45, -1.35,
23363		-0.04, -0.01, -52.27, -70.01, 0.00, 0.00, -1.57, 1.17,
23364		0.03, -52.95, 66.29, 0.32, 0.40, 1.48, 1.18, 0.04,
23365
23366		/* 724-851 */
23367		-0.01, 51.02, 67.25, 0.00, 0.00, 1.50, -1.14, -0.03,
23368		-55.66, -60.92, 0.16, -0.20, -1.36, 1.24, 0.03, -54.81,
23369		-59.20, -0.08, 0.20, -1.32, 1.23, 0.03, 51.32, -55.60,
23370		0.00, 0.00, -1.24, -1.15, -0.03, 48.29, 51.80, 0.20,
23371		-0.20, 1.16, -1.08, -0.03, -45.59, -49.00, -0.12, 0.10,
23372		-1.10, 1.02, 0.03, 40.54, -52.69, -0.04, -0.10, -1.18,
23373		-0.91, -0.02, -40.58, -49.51, -1.00, 1.00, -1.11, 0.91,
23374		0.04, 0.02, -43.76, 46.50, 0.36, 0.40, 1.04, 0.98,
23375		0.03, -0.01, 62.65, -5.00, -0.24, 0.00, -0.11, -1.40,
23376		-0.03, 0.01, -38.57, 49.59, 0.08, 0.10, 1.11, 0.86,
23377		0.02, -33.22, -44.04, 0.08, -0.10, -0.98, 0.74, 0.02,
23378		37.15, -39.90, -0.12, -0.10, -0.89, -0.83, -0.02, 36.68,
23379		-39.50, -0.04, -0.10, -0.88, -0.82, -0.02, -53.22, -3.91,
23380		-0.20, 0.00, -0.09, 1.19, 0.03, 32.43, -42.19, -0.04,
23381		-0.10, -0.94, -0.73, -0.02, -51.00, -2.30, -0.12, -0.10,
23382		0.00, 1.14, -29.53, -39.11, 0.04, 0.00, -0.87, 0.66,
23383
23384		/* 852-979 */
23385		0.02, 28.50, -38.92, -0.08, -0.10, -0.87, -0.64, -0.02,
23386		26.54, 36.95, -0.12, 0.10, 0.83, -0.59, -0.01, 26.54,
23387		34.59, 0.04, -0.10, 0.77, -0.59, -0.02, 28.35, -32.55,
23388		-0.16, 0.20, -0.73, -0.63, -0.01, -28.00, 30.40, 0.00,
23389		0.00, 0.68, 0.63, 0.01, -27.61, 29.40, 0.20, 0.20,
23390		0.66, 0.62, 0.02, 40.33, 0.40, -0.04, 0.10, 0.00,
23391		-0.90, -23.28, 31.61, -0.08, -0.10, 0.71, 0.52, 0.01,
23392		37.75, 0.80, 0.04, 0.10, 0.00, -0.84, 23.66, 25.80,
23393		0.00, 0.00, 0.58, -0.53, -0.01, 21.01, -27.91, 0.00,
23394		0.00, -0.62, -0.47, -0.01, -34.81, 2.89, 0.04, 0.00,
23395		0.00, 0.78, -23.49, -25.31, 0.00, 0.00, -0.57, 0.53,
23396		0.01, -23.47, 25.20, 0.16, 0.20, 0.56, 0.52, 0.02,
23397		19.58, 27.50, -0.12, 0.10, 0.62, -0.44, -0.01, -22.67,
23398		-24.40, -0.08, 0.10, -0.55, 0.51, 0.01, -19.97, 25.00,
23399		0.12, 0.20, 0.56, 0.45, 0.01, 21.28, -22.80, -0.08,
23400		-0.10, -0.51, -0.48, -0.01, -30.47, 0.91, 0.04, 0.00,
23401
23402		/* 980-1107 */
23403		0.00, 0.68, 18.58, 24.00, 0.04, -0.10, 0.54, -0.42,
23404		-0.01, -18.02, 24.40, -0.04, -0.10, 0.55, 0.40, 0.01,
23405		17.74, 22.50, 0.08, -0.10, 0.50, -0.40, -0.01, -19.41,
23406		20.70, 0.08, 0.10, 0.46, 0.43, 0.01, -18.64, 20.11,
23407		0.00, 0.00, 0.45, 0.42, 0.01, -16.75, 21.60, 0.04,
23408		0.10, 0.48, 0.37, 0.01, -18.42, -20.00, 0.00, 0.00,
23409		-0.45, 0.41, 0.01, -26.77, 1.41, 0.08, 0.00, 0.00,
23410		0.60, -26.17, -0.19, 0.00, 0.00, 0.00, 0.59, -15.52,
23411		20.51, 0.00, 0.00, 0.46, 0.35, 0.01, -25.42, -1.91,
23412		-0.08, 0.00, -0.04, 0.57, 0.45, -17.42, 18.10, 0.00,
23413		0.00, 0.40, 0.39, 0.01, 16.39, -17.60, -0.08, -0.10,
23414		-0.39, -0.37, -0.01, -14.37, 18.91, 0.00, 0.00, 0.42,
23415		0.32, 0.01, 23.39, -2.40, -0.12, 0.00, 0.00, -0.52,
23416		14.32, -18.50, -0.04, -0.10, -0.41, -0.32, -0.01, 15.69,
23417		17.08, 0.00, 0.00, 0.38, -0.35, -0.01, -22.99, 0.50,
23418		0.04, 0.00, 0.00, 0.51, 0.00, 0.00, 14.47, -17.60,
23419
23420		/* 1108-1235 */
23421		-0.01, 0.00, -0.39, -0.32, -13.33, 18.40, -0.04, -0.10,
23422		0.41, 0.30, 22.47, -0.60, -0.04, 0.00, 0.00, -0.50,
23423		-12.78, -17.41, 0.04, 0.00, -0.39, 0.29, 0.01, -14.10,
23424		-15.31, 0.04, 0.00, -0.34, 0.32, 0.01, 11.98, 16.21,
23425		-0.04, 0.00, 0.36, -0.27, -0.01, 19.65, -1.90, -0.08,
23426		0.00, 0.00, -0.44, 19.61, -1.50, -0.08, 0.00, 0.00,
23427		-0.44, 13.41, -14.30, -0.04, -0.10, -0.32, -0.30, -0.01,
23428		-13.29, 14.40, 0.00, 0.00, 0.32, 0.30, 0.01, 11.14,
23429		-14.40, -0.04, 0.00, -0.32, -0.25, -0.01, 12.24, -13.38,
23430		0.04, 0.00, -0.30, -0.27, -0.01, 10.07, -13.81, 0.04,
23431		0.00, -0.31, -0.23, -0.01, 10.46, 13.10, 0.08, -0.10,
23432		0.29, -0.23, -0.01, 16.55, -1.71, -0.08, 0.00, 0.00,
23433		-0.37, 9.75, -12.80, 0.00, 0.00, -0.29, -0.22, -0.01,
23434		9.11, 12.80, 0.00, 0.00, 0.29, -0.20, 0.00, 0.00,
23435		-6.44, -13.80, 0.00, 0.00, -0.31, 0.14, -9.19, -12.00,
23436		0.00, 0.00, -0.27, 0.21, -10.30, 10.90, 0.08, 0.10,
23437
23438		/* 1236-1363 */
23439		0.24, 0.23, 0.01, 14.92, -0.80, -0.04, 0.00, 0.00,
23440		-0.33, 10.02, -10.80, 0.00, 0.00, -0.24, -0.22, -0.01,
23441		-9.75, 10.40, 0.04, 0.00, 0.23, 0.22, 0.01, 9.67,
23442		-10.40, -0.04, 0.00, -0.23, -0.22, -0.01, -8.28, -11.20,
23443		0.04, 0.00, -0.25, 0.19, 13.32, -1.41, -0.08, 0.00,
23444		0.00, -0.30, 8.27, 10.50, 0.04, 0.00, 0.23, -0.19,
23445		0.00, 0.00, 13.13, 0.00, 0.00, 0.00, 0.00, -0.29,
23446		-12.93, 0.70, 0.04, 0.00, 0.00, 0.29, 7.91, -10.20,
23447		0.00, 0.00, -0.23, -0.18, -7.84, -10.00, -0.04, 0.00,
23448		-0.22, 0.18, 7.44, 9.60, 0.00, 0.00, 0.21, -0.17,
23449		-7.64, 9.40, 0.08, 0.10, 0.21, 0.17, 0.01, -11.38,
23450		0.60, 0.04, 0.00, 0.00, 0.25, -7.48, 8.30, 0.00,
23451		0.00, 0.19, 0.17, -10.98, -0.20, 0.00, 0.00, 0.00,
23452		0.25, 10.98, 0.20, 0.00, 0.00, 0.00, -0.25, 7.40,
23453		-7.90, -0.04, 0.00, -0.18, -0.17, -6.09, 8.40, -0.04,
23454		0.00, 0.19, 0.14, -6.94, -7.49, 0.00, 0.00, -0.17,
23455
23456		/* 1364-1491 */
23457		0.16, 6.92, 7.50, 0.04, 0.00, 0.17, -0.15, 6.20,
23458		8.09, 0.00, 0.00, 0.18, -0.14, -6.12, 7.80, 0.04,
23459		0.00, 0.17, 0.14, 5.85, -7.50, 0.00, 0.00, -0.17,
23460		-0.13, -6.48, 6.90, 0.08, 0.10, 0.15, 0.14, 0.01,
23461		6.32, 6.90, 0.00, 0.00, 0.15, -0.14, 5.61, -7.20,
23462		0.00, 0.00, -0.16, -0.13, 9.07, 0.00, 0.00, 0.00,
23463		0.00, -0.20, 5.25, 6.90, 0.00, 0.00, 0.15, -0.12,
23464		-8.47, -0.40, 0.00, 0.00, 0.00, 0.19, 6.32, -5.39,
23465		-1.11, 1.10, -0.12, -0.14, 0.02, 0.02, 5.73, -6.10,
23466		-0.04, 0.00, -0.14, -0.13, 4.70, 6.60, -0.04, 0.00,
23467		0.15, -0.11, -4.90, -6.40, 0.00, 0.00, -0.14, 0.11,
23468		-5.33, 5.60, 0.04, 0.10, 0.13, 0.12, 0.01, -4.81,
23469		6.00, 0.04, 0.00, 0.13, 0.11, 5.13, 5.50, 0.04,
23470		0.00, 0.12, -0.11, 4.50, 5.90, 0.00, 0.00, 0.13,
23471		-0.10, -4.22, 6.10, 0.00, 0.00, 0.14, -4.53, 5.70,
23472		0.00, 0.00, 0.13, 0.10, 4.18, 5.70, 0.00, 0.00,
23473
23474		/* 1492-1619 */
23475		0.13, -4.75, -5.19, 0.00, 0.00, -0.12, 0.11, -4.06,
23476		5.60, 0.00, 0.00, 0.13, -3.98, 5.60, -0.04, 0.00,
23477		0.13, 4.02, -5.40, 0.00, 0.00, -0.12, 4.49, -4.90,
23478		-0.04, 0.00, -0.11, -0.10, -3.62, -5.40, -0.16, 0.20,
23479		-0.12, 0.00, 0.01, 4.38, 4.80, 0.00, 0.00, 0.11,
23480		-6.40, -0.10, 0.00, 0.00, 0.00, 0.14, -3.98, 5.00,
23481		0.04, 0.00, 0.11, -3.82, -5.00, 0.00, 0.00, -0.11,
23482		-3.71, 5.07, 0.00, 0.00, 0.11, 4.14, 4.40, 0.00,
23483		0.00, 0.10, -6.01, -0.50, -0.04, 0.00, 0.00, 0.13,
23484		-4.04, 4.39, 0.00, 0.00, 0.10, 3.45, -4.72, 0.00,
23485		0.00, -0.11, 3.31, 4.71, 0.00, 0.00, 0.11, 3.26,
23486		-4.50, 0.00, 0.00, -0.10, -3.26, -4.50, 0.00, 0.00,
23487		-0.10, -3.34, -4.40, 0.00, 0.00, -0.10, -3.74, -4.00,
23488		3.70, 4.00, 3.34, -4.30, 3.30, -4.30, -3.66, 3.90,
23489		0.04, 3.66, 3.90, 0.04, -3.62, -3.90, -3.61, 3.90,
23490		-0.20, 5.30, 0.00, 0.00, 0.12, 3.06, 4.30, 3.30,
23491
23492		/* 1620-1747 */
23493		4.00, 0.40, 0.20, 3.10, 4.10, -3.06, 3.90, -3.30,
23494		-3.60, -3.30, 3.36, 0.01, 3.14, 3.40, -4.57, -0.20,
23495		0.00, 0.00, 0.00, 0.10, -2.70, -3.60, 2.94, -3.20,
23496		-2.90, 3.20, 2.47, -3.40, 2.55, -3.30, 2.80, -3.08,
23497		2.51, 3.30, -4.10, 0.30, -0.12, -0.10, 4.10, 0.20,
23498		-2.74, 3.00, 2.46, 3.23, -3.66, 1.20, -0.20, 0.20,
23499		3.74, -0.40, -2.51, -2.80, -3.74, 2.27, -2.90, 0.00,
23500		0.00, -2.50, 2.70, -2.51, 2.60, -3.50, 0.20, 3.38,
23501		-2.22, -2.50, 3.26, -0.40, 1.95, -2.60, 3.22, -0.40,
23502		-0.04, -1.79, -2.60, 1.91, 2.50, 0.74, 3.05, -0.04,
23503		0.08, 2.11, -2.30, -2.11, 2.20, -1.87, -2.40, 2.03,
23504		-2.20, -2.03, 2.20, 2.98, 0.00, 0.00, 2.98, -1.71,
23505		2.40, 2.94, -0.10, -0.12, 0.10, 1.67, 2.40, -1.79,
23506		2.30, -1.79, 2.20, -1.67, 2.20, 1.79, -2.00, 1.87,
23507		-1.90, 1.63, -2.10, -1.59, 2.10, 1.55, -2.10, -1.55,
23508		2.10, -2.59, -0.20, -1.75, -1.90, -1.75, 1.90, -1.83,
23509
23510		/* 1748-1875 */
23511		-1.80, 1.51, 2.00, -1.51, -2.00, 1.71, 1.80, 1.31,
23512		2.10, -1.43, 2.00, 1.43, 2.00, -2.43, -1.51, 1.90,
23513		-1.47, 1.90, 2.39, 0.20, -2.39, 1.39, 1.90, 1.39,
23514		-1.80, 1.47, -1.60, 1.47, -1.60, 1.43, -1.50, -1.31,
23515		1.60, 1.27, -1.60, -1.27, 1.60, 1.27, -1.60, 2.03,
23516		1.35, 1.50, -1.39, -1.40, 1.95, -0.20, -1.27, 1.49,
23517		1.19, 1.50, 1.27, 1.40, 1.15, 1.50, 1.87, -0.10,
23518		-1.12, -1.50, 1.87, -1.11, -1.50, -1.11, -1.50, 0.00,
23519		0.00, 1.19, 1.40, 1.27, -1.30, -1.27, -1.30, -1.15,
23520		1.40, -1.23, 1.30, -1.23, -1.30, 1.22, -1.29, 1.07,
23521		-1.40, 1.75, -0.20, -1.03, -1.40, -1.07, 1.20, -1.03,
23522		1.15, 1.07, 1.10, 1.51, -1.03, 1.10, 1.03, -1.10,
23523		0.00, 0.00, -1.03, -1.10, 0.91, -1.20, -0.88, -1.20,
23524		-0.88, 1.20, -0.95, 1.10, -0.95, -1.10, 1.43, -1.39,
23525		0.95, -1.00, -0.95, 1.00, -0.80, 1.10, 0.91, -1.00,
23526		-1.35, 0.88, 1.00, -0.83, 1.00, -0.91, 0.90, 0.91,
23527
23528		/* 1876-2003 */
23529		0.90, 0.88, -0.90, -0.76, -1.00, -0.76, 1.00, 0.76,
23530		1.00, -0.72, 1.00, 0.84, -0.90, 0.84, 0.90, 1.23,
23531		0.00, 0.00, -0.52, -1.10, -0.68, 1.00, 1.19, -0.20,
23532		1.19, 0.76, 0.90, 1.15, -0.10, 1.15, -0.10, 0.72,
23533		-0.90, -1.15, -1.15, 0.68, 0.90, -0.68, 0.90, -1.11,
23534		0.00, 0.00, 0.20, 0.79, 0.80, -1.11, -0.10, 0.00,
23535		0.00, -0.48, -1.00, -0.76, -0.80, -0.72, -0.80, -1.07,
23536		-0.10, 0.64, 0.80, -0.64, -0.80, 0.64, 0.80, 0.40,
23537		0.60, 0.52, -0.50, -0.60, -0.80, -0.71, 0.70, -0.99,
23538		0.99, 0.56, 0.80, -0.56, 0.80, 0.68, -0.70, 0.68,
23539		0.70, -0.95, -0.64, 0.70, 0.64, 0.70, -0.60, 0.70,
23540		-0.60, -0.70, -0.91, -0.10, -0.51, 0.76, -0.91, -0.56,
23541		0.70, 0.88, 0.88, -0.63, -0.60, 0.55, -0.60, -0.80,
23542		0.80, -0.80, -0.52, 0.60, 0.52, 0.60, 0.52, -0.60,
23543		-0.48, 0.60, 0.48, 0.60, 0.48, 0.60, -0.76, 0.44,
23544		-0.60, 0.52, -0.50, -0.52, 0.50, 0.40, 0.60, -0.40,
23545
23546		/* 2004-2131 */
23547		-0.60, 0.40, -0.60, 0.72, -0.72, -0.51, -0.50, -0.48,
23548		0.50, 0.48, -0.50, -0.48, 0.50, -0.48, 0.50, 0.48,
23549		-0.50, -0.48, -0.50, -0.68, -0.68, 0.44, 0.50, -0.64,
23550		-0.10, -0.64, -0.10, -0.40, 0.50, 0.40, 0.50, 0.40,
23551		0.50, 0.00, 0.00, -0.40, -0.50, -0.36, -0.50, 0.36,
23552		-0.50, 0.60, -0.60, 0.40, -0.40, 0.40, 0.40, -0.40,
23553		0.40, -0.40, 0.40, -0.56, -0.56, 0.36, -0.40, -0.36,
23554		0.40, 0.36, -0.40, -0.36, -0.40, 0.36, 0.40, 0.36,
23555		0.40, -0.52, 0.52, 0.52, 0.32, 0.40, -0.32, 0.40,
23556		-0.32, 0.40, -0.32, 0.40, 0.32, -0.40, -0.32, -0.40,
23557		0.32, -0.40, 0.28, -0.40, -0.28, 0.40, 0.28, -0.40,
23558		0.28, 0.40, 0.48, -0.48, 0.48, 0.36, -0.30, -0.36,
23559		-0.30, 0.00, 0.00, 0.20, 0.40, -0.44, 0.44, -0.44,
23560		-0.44, -0.44, -0.44, 0.32, -0.30, 0.32, 0.30, 0.24,
23561		0.30, -0.12, -0.10, -0.28, 0.30, 0.28, 0.30, 0.28,
23562		0.30, 0.28, -0.30, 0.28, -0.30, 0.28, -0.30, 0.28,
23563
23564		/* 2132-2259 */
23565		0.30, -0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.24,
23566		-0.30, 0.24, -0.30, -0.24, -0.30, 0.24, 0.30, 0.24,
23567		-0.30, -0.24, 0.30, 0.24, -0.30, -0.24, -0.30, 0.24,
23568		-0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, 0.20,
23569		-0.30, 0.20, -0.30, 0.20, -0.30, 0.20, 0.30, 0.20,
23570		-0.30, 0.20, -0.30, 0.20, 0.30, 0.20, 0.30, -0.20,
23571		-0.30, 0.20, -0.30, 0.20, -0.30, -0.36, -0.36, -0.36,
23572		-0.04, 0.30, 0.12, -0.10, -0.32, -0.24, 0.20, 0.24,
23573		0.20, 0.20, -0.20, -0.20, -0.20, -0.20, -0.20, 0.20,
23574		0.20, 0.20, -0.20, 0.20, 0.20, 0.20, 0.20, -0.20,
23575		-0.20, 0.00, 0.00, -0.20, -0.20, -0.20, 0.20, -0.20,
23576		0.20, 0.20, -0.20, -0.20, -0.20, 0.20, 0.20, 0.20,
23577		0.20, 0.20, -0.20, 0.20, -0.20, 0.28, 0.28, 0.28,
23578		0.28, 0.28, 0.28, -0.28, 0.28, 0.12, 0.00, 0.24,
23579		0.16, -0.20, 0.16, -0.20, 0.16, -0.20, 0.16, 0.20,
23580		-0.16, 0.20, 0.16, 0.20, -0.16, 0.20, -0.16, 0.20,
23581
23582		/* 2260-2387 */
23583		-0.16, 0.20, 0.16, -0.20, 0.16, 0.20, 0.16, -0.20,
23584		-0.16, 0.20, -0.16, -0.20, -0.16, 0.20, 0.16, 0.20,
23585		0.16, -0.20, 0.16, -0.20, 0.16, 0.20, 0.16, 0.20,
23586		0.16, 0.20, -0.16, -0.20, 0.16, 0.20, -0.16, 0.20,
23587		0.16, 0.20, -0.16, -0.20, 0.16, -0.20, 0.16, -0.20,
23588		-0.16, -0.20, 0.24, -0.24, -0.24, 0.24, 0.24, 0.12,
23589		0.20, 0.12, 0.20, -0.12, -0.20, 0.12, -0.20, 0.12,
23590		-0.20, -0.12, 0.20, -0.12, 0.20, -0.12, -0.20, 0.12,
23591		0.20, 0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12,
23592		-0.20, -0.12, 0.20, 0.12, 0.20, 0.00, 0.00, -0.12,
23593		0.20, -0.12, 0.20, 0.12, -0.20, -0.12, 0.20, 0.12,
23594		0.20, 0.00, -0.21, -0.20, 0.00, 0.00, 0.20, -0.20,
23595		-0.20, -0.20, 0.20, -0.16, -0.10, 0.00, 0.17, 0.16,
23596		0.16, 0.16, 0.16, -0.16, 0.16, 0.16, -0.16, 0.16,
23597		-0.16, 0.16, 0.12, 0.10, 0.12, -0.10, -0.12, 0.10,
23598		-0.12, 0.10, 0.12, -0.10, -0.12, 0.12, -0.12, 0.12,
23599
23600		/* 2388-2515 */
23601		-0.12, 0.12, -0.12, -0.12, -0.12, -0.12, -0.12, -0.12,
23602		-0.12, 0.12, 0.12, 0.12, 0.12, -0.12, -0.12, 0.12,
23603		0.12, 0.12, -0.12, 0.12, -0.12, -0.12, -0.12, 0.12,
23604		-0.12, -0.12, 0.12, 0.00, 0.11, 0.11,-122.67, 164.70,
23605		203.78, 273.50, 3.58, 2.74, 6.18, -4.56, 0.00, -0.04,
23606		0.00, -0.07, 57.44, -77.10, 95.82, 128.60, -1.77, -1.28,
23607		2.85, -2.14, 82.14, 89.50, 0.00, 0.00, 2.00, -1.84,
23608		-0.04, 47.73, -64.10, 23.79, 31.90, -1.45, -1.07, 0.69,
23609		-0.53, -46.38, 50.50, 0.00, 0.00, 1.13, 1.04, 0.02,
23610		-18.38, 0.00, 63.80, 0.00, 0.00, 0.41, 0.00, -1.43,
23611		59.07, 0.00, 0.00, 0.00, 0.00, -1.32, 57.28, 0.00,
23612		0.00, 0.00, 0.00, -1.28, -48.65, 0.00, -1.15, 0.00,
23613		0.00, 1.09, 0.00, 0.03, -18.30, 24.60, -17.30, -23.20,
23614		0.56, 0.41, -0.51, 0.39, -16.91, 26.90, 8.43, 13.30,
23615		0.60, 0.38, 0.31, -0.19, 1.23, -1.70, -19.13, -25.70,
23616		-0.03, -0.03, -0.58, 0.43, -0.72, 0.90, -17.34, -23.30,
23617
23618		/* 2516-2643 */
23619		0.03, 0.02, -0.52, 0.39, -19.49, -21.30, 0.00, 0.00,
23620		-0.48, 0.44, 0.01, 20.57, -20.10, 0.64, 0.70, -0.45,
23621		-0.46, 0.00, -0.01, 4.89, 5.90, -16.55, 19.90, 0.14,
23622		-0.11, 0.44, 0.37, 18.22, 19.80, 0.00, 0.00, 0.44,
23623		-0.41, -0.01, 4.89, -5.30, -16.51, -18.00, -0.11, -0.11,
23624		-0.41, 0.37, -17.86, 0.00, 17.10, 0.00, 0.00, 0.40,
23625		0.00, -0.38, 0.32, 0.00, 24.42, 0.00, 0.00, -0.01,
23626		0.00, -0.55, -23.79, 0.00, 0.00, 0.00, 0.00, 0.53,
23627		14.72, -16.00, -0.32, 0.00, -0.36, -0.33, -0.01, 0.01,
23628		3.34, -4.50, 11.86, 15.90, -0.11, -0.07, 0.35, -0.27,
23629		-3.26, 4.40, 11.62, 15.60, 0.09, 0.07, 0.35, -0.26,
23630		-19.53, 0.00, 5.09, 0.00, 0.00, 0.44, 0.00, -0.11,
23631		-13.48, 14.70, 0.00, 0.00, 0.33, 0.30, 0.01, 10.86,
23632		-14.60, 3.18, 4.30, -0.33, -0.24, 0.09, -0.07, -11.30,
23633		-15.10, 0.00, 0.00, -0.34, 0.25, 0.01, 2.03, -2.70,
23634		10.82, 14.50, -0.07, -0.05, 0.32, -0.24, 17.46, 0.00,
23635
23636		/* 2644-2771 */
23637		0.00, 0.00, 0.00, -0.39, 16.43, 0.00, 0.52, 0.00,
23638		0.00, -0.37, 0.00, -0.01, 9.35, 0.00, 13.29, 0.00,
23639		0.00, -0.21, 0.00, -0.30, -10.42, 11.40, 0.00, 0.00,
23640		0.25, 0.23, 0.01, 0.44, 0.50, -10.38, 11.30, 0.02,
23641		-0.01, 0.25, 0.23, -14.64, 0.00, 0.00, 0.00, 0.00,
23642		0.33, 0.56, 0.80, -8.67, 11.70, 0.02, -0.01, 0.26,
23643		0.19, 13.88, 0.00, -2.47, 0.00, 0.00, -0.31, 0.00,
23644		0.06, -1.99, 2.70, 7.72, 10.30, 0.06, 0.04, 0.23,
23645		-0.17, -0.20, 0.00, 13.05, 0.00, 0.00, 0.00, 0.00,
23646		-0.29, 6.92, -9.30, 3.34, 4.50, -0.21, -0.15, 0.10,
23647		-0.07, -6.60, 0.00, 10.70, 0.00, 0.00, 0.15, 0.00,
23648		-0.24, -8.04, -8.70, 0.00, 0.00, -0.19, 0.18, -10.58,
23649		0.00, -3.10, 0.00, 0.00, 0.24, 0.00, 0.07, -7.32,
23650		8.00, -0.12, -0.10, 0.18, 0.16, 1.63, 1.70, 6.96,
23651		-7.60, 0.03, -0.04, -0.17, -0.16, -3.62, 0.00, 9.86,
23652		0.00, 0.00, 0.08, 0.00, -0.22, 0.20, -0.20, -6.88,
23653
23654		/* 2772-2899 */
23655		-7.50, 0.00, 0.00, -0.17, 0.15, -8.99, 0.00, 4.02,
23656		0.00, 0.00, 0.20, 0.00, -0.09, -1.07, 1.40, -5.69,
23657		-7.70, 0.03, 0.02, -0.17, 0.13, 6.48, -7.20, -0.48,
23658		-0.50, -0.16, -0.14, -0.01, 0.01, 5.57, -7.50, 1.07,
23659		1.40, -0.17, -0.12, 0.03, -0.02, 8.71, 0.00, 3.54,
23660		0.00, 0.00, -0.19, 0.00, -0.08, 0.40, 0.00, 9.27,
23661		0.00, 0.00, -0.01, 0.00, -0.21, -6.13, 6.70, -1.19,
23662		-1.30, 0.15, 0.14, -0.03, 0.03, 5.21, -5.70, -2.51,
23663		-2.60, -0.13, -0.12, -0.06, 0.06, 5.69, -6.20, -0.12,
23664		-0.10, -0.14, -0.13, -0.01, 2.03, -2.70, 4.53, 6.10,
23665		-0.06, -0.05, 0.14, -0.10, 5.01, 5.50, -2.51, 2.70,
23666		0.12, -0.11, 0.06, 0.06, -1.91, 2.60, -4.38, -5.90,
23667		0.06, 0.04, -0.13, 0.10, 4.65, -6.30, 0.00, 0.00,
23668		-0.14, -0.10, -5.29, 5.70, 0.00, 0.00, 0.13, 0.12,
23669		-2.23, -4.00, -4.65, 4.20, -0.09, 0.05, 0.10, 0.10,
23670		-4.53, 6.10, 0.00, 0.00, 0.14, 0.10, 2.47, 2.70,
23671
23672		/* 2900-3027 */
23673		-4.46, 4.90, 0.06, -0.06, 0.11, 0.10, -5.05, 5.50,
23674		0.84, 0.90, 0.12, 0.11, 0.02, -0.02, 4.97, -5.40,
23675		-1.71, 0.00, -0.12, -0.11, 0.00, 0.04, -0.99, -1.30,
23676		4.22, -5.70, -0.03, 0.02, -0.13, -0.09, 0.99, 1.40,
23677		4.22, -5.60, 0.03, -0.02, -0.13, -0.09, -4.69, -5.20,
23678		0.00, 0.00, -0.12, 0.10, -3.42, 0.00, 6.09, 0.00,
23679		0.00, 0.08, 0.00, -0.14, -4.65, -5.10, 0.00, 0.00,
23680		-0.11, 0.10, 0.00, 0.00, -4.53, -5.00, 0.00, 0.00,
23681		-0.11, 0.10, -2.43, -2.70, -3.82, 4.20, -0.06, 0.05,
23682		0.10, 0.09, 0.00, 0.00, -4.53, 4.90, 0.00, 0.00,
23683		0.11, 0.10, -4.49, -4.90, 0.00, 0.00, -0.11, 0.10,
23684		2.67, -2.90, -3.62, -3.90, -0.06, -0.06, -0.09, 0.08,
23685		3.94, -5.30, 0.00, 0.00, -0.12, -3.38, 3.70, -2.78,
23686		-3.10, 0.08, 0.08, -0.07, 0.06, 3.18, -3.50, -2.82,
23687		-3.10, -0.08, -0.07, -0.07, 0.06, -5.77, 0.00, 1.87,
23688		0.00, 0.00, 0.13, 0.00, -0.04, 3.54, -4.80, -0.64,
23689
23690		/* 3028-3155 */
23691		-0.90, -0.11, 0.00, -0.02, -3.50, -4.70, 0.68, -0.90,
23692		-0.11, 0.00, -0.02, 5.49, 0.00, 0.00, 0.00, 0.00,
23693		-0.12, 1.83, -2.50, 2.63, 3.50, -0.06, 0.00, 0.08,
23694		3.02, -4.10, 0.68, 0.90, -0.09, 0.00, 0.02, 0.00,
23695		0.00, 5.21, 0.00, 0.00, 0.00, 0.00, -0.12, -3.54,
23696		3.80, 2.70, 3.60, -1.35, 1.80, 0.08, 0.00, 0.04,
23697		-2.90, 3.90, 0.68, 0.90, 0.09, 0.00, 0.02, 0.80,
23698		-1.10, -2.78, -3.70, -0.02, 0.00, -0.08, 4.10, 0.00,
23699		-2.39, 0.00, 0.00, -0.09, 0.00, 0.05, -1.59, 2.10,
23700		2.27, 3.00, 0.05, 0.00, 0.07, -2.63, 3.50, -0.48,
23701		-0.60, -2.94, -3.20, -2.94, 3.20, 2.27, -3.00, -1.11,
23702		-1.50, -0.07, 0.00, -0.03, -0.56, -0.80, -2.35, 3.10,
23703		0.00, -0.60, -3.42, 1.90, -0.12, -0.10, 2.63, -2.90,
23704		2.51, 2.80, -0.64, 0.70, -0.48, -0.60, 2.19, -2.90,
23705		0.24, -0.30, 2.15, 2.90, 2.15, -2.90, 0.52, 0.70,
23706		2.07, -2.80, -3.10, 0.00, 1.79, 0.00, 0.00, 0.07,
23707
23708		/* 3156-3283 */
23709		0.00, -0.04, 0.88, 0.00, -3.46, 2.11, 2.80, -0.36,
23710		0.50, 3.54, -0.20, -3.50, -1.39, 1.50, -1.91, -2.10,
23711		-1.47, 2.00, 1.39, 1.90, 2.07, -2.30, 0.91, 1.00,
23712		1.99, -2.70, 3.30, 0.00, 0.60, -0.44, -0.70, -1.95,
23713		2.60, 2.15, -2.40, -0.60, -0.70, 3.30, 0.84, 0.00,
23714		-3.10, -3.10, 0.00, -0.72, -0.32, 0.40, -1.87, -2.50,
23715		1.87, -2.50, 0.32, 0.40, -0.24, 0.30, -1.87, -2.50,
23716		-0.24, -0.30, 1.87, -2.50, -2.70, 0.00, 1.55, 2.03,
23717		2.20, -2.98, -1.99, -2.20, 0.12, -0.10, -0.40, 0.50,
23718		1.59, 2.10, 0.00, 0.00, -1.79, 2.00, -1.03, 1.40,
23719		-1.15, -1.60, 0.32, 0.50, 1.39, -1.90, 2.35, -1.27,
23720		1.70, 0.60, 0.80, -0.32, -0.40, 1.35, -1.80, 0.44,
23721		0.00, 2.23, -0.84, 0.90, -1.27, -1.40, -1.47, 1.60,
23722		-0.28, -0.30, -0.28, 0.40, -1.27, -1.70, 0.28, -0.40,
23723		-1.43, -1.50, 0.00, 0.00, -1.27, -1.70, 2.11, -0.32,
23724		-0.40, -1.23, 1.60, 1.19, -1.30, -0.72, -0.80, 0.72,
23725
23726		/* 3284-3411 */
23727		-0.80, -1.15, -1.30, -1.35, -1.50, -1.19, -1.60, -0.12,
23728		0.20, 1.79, 0.00, -0.88, -0.28, 0.40, 1.11, 1.50,
23729		-1.83, 0.00, 0.56, -0.12, 0.10, -1.27, -1.40, 0.00,
23730		0.00, 1.15, 1.50, -0.12, 0.20, 1.11, 1.50, 0.36,
23731		-0.50, -1.07, -1.40, -1.11, 1.50, 1.67, 0.00, 0.80,
23732		-1.11, 0.00, 1.43, 1.23, -1.30, -0.24, -1.19, -1.30,
23733		-0.24, 0.20, -0.44, -0.90, -0.95, 1.10, 1.07, -1.40,
23734		1.15, -1.30, 1.03, -1.10, -0.56, -0.60, -0.68, 0.90,
23735		-0.76, -1.00, -0.24, -0.30, 0.95, -1.30, 0.56, 0.70,
23736		0.84, -1.10, -0.56, 0.00, -1.55, 0.91, -1.30, 0.28,
23737		0.30, 0.16, -0.20, 0.95, 1.30, 0.40, -0.50, -0.88,
23738		-1.20, 0.95, -1.10, -0.48, -0.50, 0.00, 0.00, -1.07,
23739		1.20, 0.44, -0.50, 0.95, 1.10, 0.00, 0.00, 0.92,
23740		-1.30, 0.95, 1.00, -0.52, 0.60, 1.59, 0.24, -0.40,
23741		0.91, 1.20, 0.84, -1.10, -0.44, -0.60, 0.84, 1.10,
23742		-0.44, 0.60, -0.44, 0.60, -0.84, -1.10, -0.80, 0.00,
23743
23744		/* 3412-3539 */
23745		1.35, 0.76, 0.20, -0.91, -1.00, 0.20, -0.30, -0.91,
23746		-1.20, -0.95, 1.00, -0.48, -0.50, 0.88, 1.00, 0.48,
23747		-0.50, -0.95, -1.10, 0.20, -0.20, -0.99, 1.10, -0.84,
23748		1.10, -0.24, -0.30, 0.20, -0.30, 0.84, 1.10, -1.39,
23749		0.00, -0.28, -0.16, 0.20, 0.84, 1.10, 0.00, 0.00,
23750		1.39, 0.00, 0.00, -0.95, 1.00, 1.35, -0.99, 0.00,
23751		0.88, -0.52, 0.00, -1.19, 0.20, 0.20, 0.76, -1.00,
23752		0.00, 0.00, 0.76, 1.00, 0.00, 0.00, 0.76, 1.00,
23753		-0.76, 1.00, 0.00, 0.00, 1.23, 0.76, 0.80, -0.32,
23754		0.40, -0.72, 0.80, -0.40, -0.40, 0.00, 0.00, -0.80,
23755		-0.90, -0.68, 0.90, -0.16, -0.20, -0.16, -0.20, 0.68,
23756		-0.90, -0.36, 0.50, -0.56, -0.80, 0.72, -0.90, 0.44,
23757		-0.60, -0.48, -0.70, -0.16, 0.00, -1.11, 0.32, 0.00,
23758		-1.07, 0.60, -0.80, -0.28, -0.40, -0.64, 0.00, 0.91,
23759		1.11, 0.64, -0.90, 0.76, -0.80, 0.00, 0.00, -0.76,
23760		-0.80, 1.03, 0.00, -0.36, -0.64, -0.70, 0.36, -0.40,
23761
23762		/* 3540-3667 */
23763		1.07, 0.36, -0.50, -0.52, -0.70, 0.60, 0.00, 0.88,
23764		0.95, 0.00, 0.48, 0.16, -0.20, 0.60, 0.80, 0.16,
23765		-0.20, -0.60, -0.80, 0.00, -1.00, 0.12, 0.20, 0.16,
23766		-0.20, 0.68, 0.70, 0.59, -0.80, -0.99, -0.56, -0.60,
23767		0.36, -0.40, -0.68, -0.70, -0.68, -0.70, -0.36, -0.50,
23768		-0.44, 0.60, 0.64, 0.70, -0.12, 0.10, -0.52, 0.60,
23769		0.36, 0.40, 0.00, 0.00, 0.95, -0.84, 0.00, 0.44,
23770		0.56, 0.60, 0.32, -0.30, 0.00, 0.00, 0.60, 0.70,
23771		0.00, 0.00, 0.60, 0.70, -0.12, -0.20, 0.52, -0.70,
23772		0.00, 0.00, 0.56, 0.70, -0.12, 0.10, -0.52, -0.70,
23773		0.00, 0.00, 0.88, -0.76, 0.00, -0.44, 0.00, 0.00,
23774		-0.52, -0.70, 0.52, -0.70, 0.36, -0.40, -0.44, -0.50,
23775		0.00, 0.00, 0.60, 0.60, 0.84, 0.00, 0.12, -0.24,
23776		0.00, 0.80, -0.56, 0.60, -0.32, -0.30, 0.48, -0.50,
23777		0.28, -0.30, -0.48, -0.50, 0.12, 0.20, 0.48, -0.60,
23778		0.48, 0.60, -0.12, 0.20, 0.24, 0.00, 0.76, -0.52,
23779
23780		/* 3668-3795 */
23781		-0.60, -0.52, 0.60, 0.48, -0.50, -0.24, -0.30, 0.12,
23782		-0.10, 0.48, 0.60, 0.52, -0.20, 0.36, 0.40, -0.44,
23783		0.50, -0.24, -0.30, -0.48, -0.60, -0.44, -0.60, -0.12,
23784		0.10, 0.76, 0.76, 0.20, -0.20, 0.48, 0.50, 0.40,
23785		-0.50, -0.24, -0.30, 0.44, -0.60, 0.44, -0.60, 0.36,
23786		0.00, -0.64, 0.72, 0.00, -0.12, 0.00, -0.10, -0.40,
23787		-0.60, -0.20, -0.20, -0.44, 0.50, -0.44, 0.50, 0.20,
23788		0.20, -0.44, -0.50, 0.20, -0.20, -0.20, 0.20, -0.44,
23789		-0.50, 0.64, 0.00, 0.32, -0.36, 0.50, -0.20, -0.30,
23790		0.12, -0.10, 0.48, 0.50, -0.12, 0.30, -0.36, -0.50,
23791		0.00, 0.00, 0.48, 0.50, -0.48, 0.50, 0.68, 0.00,
23792		-0.12, 0.56, -0.40, 0.44, -0.50, -0.12, -0.10, 0.24,
23793		0.30, -0.40, 0.40, 0.64, 0.00, -0.24, 0.64, 0.00,
23794		-0.20, 0.00, 0.00, 0.44, -0.50, 0.44, 0.50, -0.12,
23795		0.20, -0.36, -0.50, 0.12, 0.00, 0.64, -0.40, 0.50,
23796		0.00, 0.10, 0.00, 0.00, -0.40, 0.50, 0.00, 0.00,
23797
23798		/* 3796-3923 */
23799		-0.40, -0.50, 0.56, 0.00, 0.28, 0.00, 0.10, 0.36,
23800		0.50, 0.00, -0.10, 0.36, -0.50, 0.36, 0.50, 0.00,
23801		-0.10, 0.24, -0.20, -0.36, -0.40, 0.16, 0.20, 0.40,
23802		-0.40, 0.00, 0.00, -0.36, -0.50, -0.36, -0.50, -0.32,
23803		-0.50, -0.12, 0.10, 0.20, 0.20, -0.36, 0.40, -0.60,
23804		0.60, 0.28, 0.00, 0.52, 0.12, -0.10, 0.40, 0.40,
23805		0.00, -0.50, 0.20, -0.20, -0.32, 0.40, 0.16, 0.20,
23806		-0.16, 0.20, 0.32, 0.40, 0.56, 0.00, -0.12, 0.32,
23807		-0.40, -0.16, -0.20, 0.00, 0.00, 0.40, 0.40, -0.40,
23808		-0.40, -0.40, 0.40, -0.36, 0.40, 0.12, 0.10, 0.00,
23809		0.10, 0.36, 0.40, 0.00, -0.10, 0.36, 0.40, -0.36,
23810		0.40, 0.00, 0.10, 0.32, 0.00, 0.44, 0.12, 0.20,
23811		0.28, -0.40, 0.00, 0.00, 0.36, 0.40, 0.32, -0.40,
23812		-0.16, 0.12, 0.10, 0.32, -0.40, 0.20, 0.30, -0.24,
23813		0.30, 0.00, 0.10, 0.32, 0.40, 0.00, -0.10, -0.32,
23814		-0.40, -0.32, 0.40, 0.00, 0.10, -0.52, -0.52, 0.52,
23815
23816		/* 3924-4051 */
23817		0.32, -0.40, 0.00, 0.00, 0.32, 0.40, 0.32, -0.40,
23818		0.00, 0.00, -0.32, -0.40, -0.32, 0.40, 0.32, 0.40,
23819		0.00, 0.00, 0.32, 0.40, 0.00, 0.00, -0.32, -0.40,
23820		0.00, 0.00, 0.32, 0.40, 0.16, 0.20, 0.32, -0.30,
23821		-0.16, 0.00, -0.48, -0.20, 0.20, -0.28, -0.30, 0.28,
23822		-0.40, 0.00, 0.00, 0.28, -0.40, 0.00, 0.00, 0.28,
23823		-0.40, 0.00, 0.00, -0.28, -0.40, 0.28, 0.40, -0.28,
23824		-0.40, -0.48, -0.20, 0.20, 0.24, 0.30, 0.44, 0.00,
23825		0.16, 0.24, 0.30, 0.16, -0.20, 0.24, 0.30, -0.12,
23826		0.20, 0.20, 0.30, -0.16, 0.20, 0.00, 0.00, 0.44,
23827		-0.32, 0.30, 0.24, 0.00, -0.36, 0.36, 0.00, 0.24,
23828		0.12, -0.20, 0.20, 0.30, -0.12, 0.00, -0.28, 0.30,
23829		-0.24, 0.30, 0.12, 0.10, -0.28, -0.30, -0.28, 0.30,
23830		0.00, 0.00, -0.28, -0.30, 0.00, 0.00, -0.28, -0.30,
23831		0.00, 0.00, 0.28, 0.30, 0.00, 0.00, -0.28, -0.30,
23832		-0.28, 0.30, 0.00, 0.00, -0.28, -0.30, 0.00, 0.00,
23833
23834		/* 4052-4179 */
23835		0.28, 0.30, 0.00, 0.00, -0.28, 0.30, 0.28, -0.30,
23836		-0.28, 0.30, 0.40, 0.40, -0.24, 0.30, 0.00, -0.10,
23837		0.16, 0.00, 0.36, -0.20, 0.30, -0.12, -0.10, -0.24,
23838		-0.30, 0.00, 0.00, -0.24, 0.30, -0.24, 0.30, 0.00,
23839		0.00, -0.24, 0.30, -0.24, 0.30, 0.24, -0.30, 0.00,
23840		0.00, 0.24, -0.30, 0.00, 0.00, 0.24, 0.30, 0.24,
23841		-0.30, 0.24, 0.30, -0.24, 0.30, -0.24, 0.30, -0.20,
23842		0.20, -0.16, -0.20, 0.00, 0.00, -0.32, 0.20, 0.00,
23843		0.10, 0.20, -0.30, 0.20, -0.20, 0.12, 0.20, -0.16,
23844		0.20, 0.16, 0.20, 0.20, 0.30, 0.20, 0.30, 0.00,
23845		0.00, -0.20, 0.30, 0.00, 0.00, 0.20, 0.30, -0.20,
23846		-0.30, -0.20, -0.30, 0.20, -0.30, 0.00, 0.00, 0.20,
23847		0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20,
23848		0.30, 0.00, 0.00, 0.20, 0.30, 0.00, 0.00, 0.20,
23849		-0.30, 0.00, 0.00, -0.20, -0.30, 0.00, 0.00, -0.20,
23850		0.30, 0.00, 0.00, -0.20, 0.30, 0.00, 0.00, 0.36,
23851
23852		/* 4180-4307 */
23853		0.00, 0.00, 0.36, 0.12, 0.10, -0.24, 0.20, 0.12,
23854		-0.20, -0.16, -0.20, -0.13, 0.10, 0.22, 0.21, 0.20,
23855		0.00, -0.28, 0.32, 0.00, -0.12, -0.20, -0.20, 0.12,
23856		-0.10, 0.12, 0.10, -0.20, 0.20, 0.00, 0.00, -0.32,
23857		0.32, 0.00, 0.00, 0.32, 0.32, 0.00, 0.00, -0.24,
23858		-0.20, 0.24, 0.20, 0.20, 0.00, -0.24, 0.00, 0.00,
23859		-0.24, -0.20, 0.00, 0.00, 0.24, 0.20, -0.24, -0.20,
23860		0.00, 0.00, -0.24, 0.20, 0.16, -0.20, 0.12, 0.10,
23861		0.20, 0.20, 0.00, -0.10, -0.12, 0.10, -0.16, -0.20,
23862		-0.12, -0.10, -0.16, 0.20, 0.20, 0.20, 0.00, 0.00,
23863		-0.20, 0.20, -0.20, 0.20, -0.20, 0.20, -0.20, 0.20,
23864		0.20, -0.20, -0.20, -0.20, 0.00, 0.00, -0.20, 0.20,
23865		0.20, 0.00, -0.20, 0.00, 0.00, -0.20, 0.20, -0.20,
23866		0.20, -0.20, -0.20, -0.20, -0.20, 0.00, 0.00, 0.20,
23867		0.20, 0.20, 0.20, 0.12, -0.20, -0.12, -0.10, 0.28,
23868		-0.28, 0.16, -0.20, 0.00, -0.10, 0.00, 0.10, -0.16,
23869
23870		/* 4308-4435 */
23871		0.20, 0.00, -0.10, -0.16, -0.20, 0.00, -0.10, 0.16,
23872		-0.20, 0.16, -0.20, 0.00, 0.00, 0.16, 0.20, -0.16,
23873		0.20, 0.00, 0.00, 0.16, 0.20, 0.16, -0.20, 0.16,
23874		-0.20, -0.16, 0.20, 0.16, -0.20, 0.00, 0.00, 0.16,
23875		0.20, 0.00, 0.00, 0.16, 0.20, 0.00, 0.00, -0.16,
23876		-0.20, 0.16, -0.20, -0.16, -0.20, 0.00, 0.00, -0.16,
23877		-0.20, 0.00, 0.00, -0.16, 0.20, 0.00, 0.00, 0.16,
23878		-0.20, 0.16, 0.20, 0.16, 0.20, 0.00, 0.00, -0.16,
23879		-0.20, 0.00, 0.00, -0.16, -0.20, 0.00, 0.00, 0.16,
23880		0.20, 0.16, 0.20, 0.00, 0.00, 0.16, 0.20, 0.16,
23881		-0.20, 0.16, 0.20, 0.00, 0.00, -0.16, 0.20, 0.00,
23882		0.10, 0.12, -0.20, 0.12, -0.20, 0.00, -0.10, 0.00,
23883		-0.10, 0.12, 0.20, 0.00, -0.10, -0.12, 0.20, -0.15,
23884		0.20, -0.24, 0.24, 0.00, 0.00, 0.24, 0.24, 0.12,
23885		-0.20, -0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.12,
23886		-0.20, 0.12, 0.20, 0.12, 0.20, 0.12, 0.20, 0.12,
23887
23888		/* 4436-4563 */
23889		-0.20, -0.12, 0.20, 0.00, 0.00, 0.12, 0.20, 0.12,
23890		0.00, -0.20, 0.00, 0.00, -0.12, -0.20, 0.12, -0.20,
23891		0.00, 0.00, 0.12, 0.20, -0.12, 0.20, -0.12, 0.20,
23892		0.12, -0.20, 0.00, 0.00, 0.12, 0.20, 0.20, 0.00,
23893		0.12, 0.00, 0.00, -0.12, 0.20, 0.00, 0.00, -0.12,
23894		-0.20, 0.00, 0.00, -0.12, -0.20, -0.12, -0.20, 0.00,
23895		0.00, 0.12, -0.20, 0.12, -0.20, 0.12, 0.20, -0.12,
23896		-0.20, 0.00, 0.00, 0.12, -0.20, 0.12, -0.20, 0.12,
23897		0.20, 0.12, 0.00, 0.20, -0.12, -0.20, 0.00, 0.00,
23898		0.12, 0.20, -0.16, 0.00, 0.16, -0.20, 0.20, 0.00,
23899		0.00, -0.20, 0.00, 0.00, -0.20, 0.20, 0.00, 0.00,
23900		0.20, 0.20, -0.20, 0.00, 0.00, -0.20, 0.12, 0.00,
23901		-0.16, 0.20, 0.00, 0.00, 0.20, 0.12, -0.10, 0.00,
23902		0.10, 0.16, -0.16, -0.16, -0.16, -0.16, -0.16, 0.00,
23903		0.00, -0.16, 0.00, 0.00, -0.16, -0.16, -0.16, 0.00,
23904		0.00, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00, 0.16,
23905
23906		/* 4564-4691 */
23907		0.00, 0.00, 0.16, 0.16, 0.00, 0.00, -0.16, 0.00,
23908		0.00, -0.16, -0.16, 0.00, 0.00, 0.16, 0.00, 0.00,
23909		-0.16, -0.16, 0.00, 0.00, -0.16, -0.16, 0.12, 0.10,
23910		0.12, -0.10, 0.12, 0.10, 0.00, 0.00, 0.12, 0.10,
23911		-0.12, 0.10, 0.00, 0.00, 0.12, 0.10, 0.12, -0.10,
23912		0.00, 0.00, -0.12, -0.10, 0.00, 0.00, 0.12, 0.10,
23913		0.12, 0.00, 0.00, 0.12, 0.00, 0.00, -0.12, 0.00,
23914		0.00, 0.12, 0.12, 0.12, 0.12, 0.12, 0.00, 0.00,
23915		0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, 0.12,
23916		0.00, 0.00, 0.12, -0.12, -0.12, 0.12, 0.12, -0.12,
23917		-0.12, 0.00, 0.00, 0.12, -0.12, 0.12, 0.12, -0.12,
23918		-0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12,
23919		0.12, 0.00, 0.00, 0.12, 0.00, 0.00, 0.12, 0.00,
23920		0.00, 0.12, -0.12, 0.00, 0.00, -0.12, 0.12, -0.12,
23921		-0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.12, -0.12,
23922		0.00, 0.00, -0.12, -0.12, -0.12, 0.00, 0.00, -0.12,
23923
23924		/* 4692-NA */
23925		-0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00, -0.12,
23926		-0.12, -0.12, -0.12, 0.12, 0.00, 0.00, 0.12, -0.12,
23927		0.00, 0.00, -0.12, -0.12, 0.00, 0.00, 0.12, -0.12,
23928		-0.12, -0.12, -0.12, 0.12, 0.12, -0.12, -0.12, 0.00,
23929		0.00, -0.12, 0.00, 0.00, -0.12, 0.12, 0.00, 0.00,
23930		0.12, 0.00, 0.00, -0.12, -0.12, 0.00, 0.00, -0.12,
23931		-0.12, 0.12, 0.00, 0.00, 0.12, 0.12, 0.00, 0.00,
23932		0.12, 0.00, 0.00, 0.12, 0.12, 0.08, 0.00, 0.04
23933		};
23934
23935		/* Number of amplitude coefficients */
23936	2	final int NA = a.length;
23937
23938		/* Amplitude usage: X or Y, sin or cos, power of T. */
23939	2	final int jaxy[] = {0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1};
23940	2	final int jasc[] = {0,1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0,1,1,0};
23941	2	final int japt[] = {0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4};
23942
23943		/* Miscellaneous */
23944	2	double t, w, pt[] = new double[MAXPT+1], fa[] = new double[14], xypr[] = new double[2], xypl[] = new double[2], xyls[] = new double[2], arg,
23945	2	sc[] = new double[2];
23946		int jpt, i, j, jxy, ialast, ifreq, m, ia, jsc;
23947
23948		/--------------------------------------------------------------------/
23949
23950		/* Interval between fundamental date J2000.0 and given date (JC). */
23951	2	t = ((date1 - DJ00) + date2) / DJC;
23952
23953		/* Powers of T. */
23954	2	w = 1.0;
23955	14	for (jpt = 0; jpt <= MAXPT; jpt++) {
23956	12	pt[jpt] = w;
23957	12	w *= t;
23958		}
23959
23960		/* Initialize totals in X and Y: polynomial, luni-solar, planetary. */
23961	6	for (jxy = 0; jxy < 2; jxy++) {
23962	4	xypr[jxy] = 0.0;
23963	4	xyls[jxy] = 0.0;
23964	4	xypl[jxy] = 0.0;
23965		}
23966
23967		/* --------------------------------- */
23968		/* Fundamental arguments (IERS 2003) */
23969		/* --------------------------------- */
23970
23971		/* Mean anomaly of the Moon. */
23972	2	fa[0] = jauFal03(t);
23973
23974		/* Mean anomaly of the Sun. */
23975	2	fa[1] = jauFalp03(t);
23976
23977		/* Mean argument of the latitude of the Moon. */
23978	2	fa[2] = jauFaf03(t);
23979
23980		/* Mean elongation of the Moon from the Sun. */
23981	2	fa[3] = jauFad03(t);
23982
23983		/* Mean longitude of the ascending node of the Moon. */
23984	2	fa[4] = jauFaom03(t);
23985
23986		/* Planetary longitudes, Mercury through Neptune. */
23987	2	fa[5] = jauFame03(t);
23988	2	fa[6] = jauFave03(t);
23989	2	fa[7] = jauFae03(t);
23990	2	fa[8] = jauFama03(t);
23991	2	fa[9] = jauFaju03(t);
23992	2	fa[10] = jauFasa03(t);
23993	2	fa[11] = jauFaur03(t);
23994	2	fa[12] = jauFane03(t);
23995
23996		/* General accumulated precession in longitude. */
23997	2	fa[13] = jauFapa03(t);
23998
23999		/* -------------------------------------- */
24000		/* Polynomial part of precession-nutation */
24001		/* -------------------------------------- */
24002
24003	6	for (jxy = 0; jxy < 2; jxy++) {
24004	28	for (j = MAXPT; j >= 0; j--) {
24005	24	xypr[jxy] += xyp[jxy][j] * pt[j];
24006		}
24007		}
24008
24009		/* ---------------------------------- */
24010		/* Nutation periodic terms, planetary */
24011		/* ---------------------------------- */
24012
24013		/* Work backwards through the coefficients per frequency list. */
24014	2	ialast = NA;
24015	1314	for (ifreq = NFPL-1; ifreq >= 0; ifreq--) {
24016
24017		/* Obtain the argument functions. */
24018	1312	arg = 0.0;
24019	19680	for (i = 0; i < 14; i++) {
24020	18368	m = mfapl[ifreq][i];
24021	18368	if (m != 0) arg += (double)m * fa[i];
24022		}
24023	1312	sc[0] = sin(arg);
24024	1312	sc[1] = cos(arg);
24025
24026		/* Work backwards through the amplitudes at this frequency. */
24027	1312	ia = nc[ifreq+NFLS];
24028	5988	for (i = ialast; i >= ia; i--) {
24029
24030		/* Coefficient number (0 = 1st). */
24031	4676	j = i-ia;
24032
24033		/* X or Y. */
24034	4676	jxy = jaxy[j];
24035
24036		/* Sin or cos. */
24037	4676	jsc = jasc[j];
24038
24039		/* Power of T. */
24040	4676	jpt = japt[j];
24041
24042		/* Accumulate the component. */
24043	4676	xypl[jxy] += a[i-1] * sc[jsc] * pt[jpt];
24044		}
24045	1312	ialast = ia-1;
24046		}
24047
24048		/* ----------------------------------- */
24049		/* Nutation periodic terms, luni-solar */
24050		/* ----------------------------------- */
24051
24052		/* Continue working backwards through the number of coefficients list. */
24053	1308	for (ifreq = NFLS-1; ifreq >= 0; ifreq--) {
24054
24055		/* Obtain the argument functions. */
24056	1306	arg = 0.0;
24057	7836	for (i = 0; i < 5; i++) {
24058	6530	m = mfals[ifreq][i];
24059	6530	if (m != 0) arg += (double)m * fa[i];
24060		}
24061	1306	sc[0] = sin(arg);
24062	1306	sc[1] = cos(arg);
24063
24064		/* Work backwards through the amplitudes at this frequency. */
24065	1306	ia = nc[ifreq];
24066	6140	for (i = ialast; i >= ia; i--) {
24067
24068		/* Coefficient number (0 = 1st). */
24069	4834	j = i-ia;
24070
24071		/* X or Y. */
24072	4834	jxy = jaxy[j];
24073
24074		/* Sin or cos. */
24075	4834	jsc = jasc[j];
24076
24077		/* Power of T. */
24078	4834	jpt = japt[j];
24079
24080		/* Accumulate the component. */
24081	4834	xyls[jxy] += a[i-1] * sc[jsc] * pt[jpt];
24082		}
24083	1306	ialast = ia-1;
24084		}
24085
24086		/* ------------------------------------ */
24087		/* Results: CIP unit vector components */
24088		/* ------------------------------------ */
24089
24090	2	double x = DAS2R * (xypr[0] + (xyls[0] + xypl[0]) / 1e6);
24091	2	double y = DAS2R * (xypr[1] + (xyls[1] + xypl[1]) / 1e6);
24092
24093	2	return new CelestialIntermediatePole(x, y);
24094
24095		}
24096
24097
24098		/**
24099		* For a given TT date, compute the X,Y coordinates of the Celestial
24100		* Intermediate Pole and the CIO locator s, using the IAU 2000A
24101		* precession-nutation model.
24102		*
24103		*<p>This function is derived from the International Astronomical Union's
24104		* SOFA (Standards Of Fundamental Astronomy) software collection.
24105		*
24106		*<p>Status: support function.
24107		*
24108		*<!-- Given: -->
24109		* @param date1 double TT as a 2-part Julian Date (Note 1)
24110		* @param date2 double TT as a 2-part Julian Date (Note 1)
24111		*
24112		*<!-- Returned: -->
24113		* @return x double <u>returned</u> Celestial Intermediate Pole (Note 2)
24114		* y double <u>returned</u> Celestial Intermediate Pole (Note 2)
24115		* s double <u>returned</u> the CIO locator s (Note 2)
24116		*
24117		* <p>Notes:
24118		* <ol>
24119		*
24120		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
24121		* convenient way between the two arguments. For example,
24122		* JD(TT)=2450123.7 could be expressed in any of these ways,
24123		* among others:
24124		*<pre>
24125		* date1 date2
24126		*
24127		* 2450123.7 0.0 (JD method)
24128		* 2451545.0 -1421.3 (J2000 method)
24129		* 2400000.5 50123.2 (MJD method)
24130		* 2450123.5 0.2 (date & time method)
24131		*</pre>
24132		* The JD method is the most natural and convenient to use in
24133		* cases where the loss of several decimal digits of resolution
24134		* is acceptable. The J2000 method is best matched to the way
24135		* the argument is handled internally and will deliver the
24136		* optimum resolution. The MJD method and the date & time methods
24137		* are both good compromises between resolution and convenience.
24138		*
24139		* <li> The Celestial Intermediate Pole coordinates are the x,y
24140		* components of the unit vector in the Geocentric Celestial
24141		* Reference System.
24142		*
24143		* <li> The CIO locator s (in radians) positions the Celestial
24144		* Intermediate Origin on the equator of the CIP.
24145		*
24146		* <li> A faster, but slightly less accurate result (about 1 mas for
24147		* X,Y), can be obtained by using instead the jauXys00b function.
24148		*</ol>
24149		*<p>Called:<ul>
24150		* <li>{@link #jauPnm00a} classical NPB matrix, IAU 2000A
24151		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
24152		* <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
24153		* </ul>
24154		*<p>Reference:
24155		*
24156		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
24157		* IERS Technical Note No. 32, BKG (2004)
24158		*
24159		*@version 2008 May 12
24160		*
24161		* @since Release 20101201
24162		*
24163		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24164		*/
24165		public static ICRFrame jauXys00a(double date1, double date2)
24166		{
24167
24168		/* Form the bias-precession-nutation matrix, IAU 2000A. */
24169	2	double rbpn[][] = jauPnm00a(date1, date2);
24170
24171		/* Extract X,Y. */
24172	2	CelestialIntermediatePole cip = jauBpn2xy(rbpn);
24173
24174		/* Obtain s. */
24175	2	double s = jauS00(date1, date2, cip.x, cip.y);
24176
24177	2	return new ICRFrame(cip, s);
24178
24179		}
24180
24181
24182		/**
24183		* The Celestial Intermediate Pole coordinates are the x,y
24184		* components of the unit vector in the Geocentric Celestial
24185		* Reference System.
24186		*
24187		* The CIO locator s (in radians) positions the Celestial
24188		* Intermediate Origin on the equator of the CIP.
24189
24190		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 1 Feb 2010
24191		*
24192		* @since AIDA Stage 1
24193		*/
24194		public static class ICRFrame {
24195		public CelestialIntermediatePole cip;
24196		public double s;
24197	6	public ICRFrame(CelestialIntermediatePole cip, double s) {
24198	6	this.cip = cip;
24199	6	this.s = s;
24200	6	}
24201		}
24202		/**
24203		* For a given TT date, compute the X,Y coordinates of the Celestial
24204		* Intermediate Pole and the CIO locator s, using the IAU 2000B
24205		* precession-nutation model.
24206		*
24207		*<p>This function is derived from the International Astronomical Union's
24208		* SOFA (Standards Of Fundamental Astronomy) software collection.
24209		*
24210		*<p>Status: support function.
24211		*
24212		*<!-- Given: -->
24213		* @param date1 double TT as a 2-part Julian Date (Note 1)
24214		* @param date2 double TT as a 2-part Julian Date (Note 1)
24215		*
24216		*<!-- Returned: -->
24217		* @return x double <u>returned</u> Celestial Intermediate Pole (Note 2)
24218		* y double <u>returned</u> Celestial Intermediate Pole (Note 2)
24219		* s double <u>returned</u> the CIO locator s (Note 2)
24220		*
24221		* <p>Notes:
24222		* <ol>
24223		*
24224		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
24225		* convenient way between the two arguments. For example,
24226		* JD(TT)=2450123.7 could be expressed in any of these ways,
24227		* among others:
24228		*<pre>
24229		* date1 date2
24230		*
24231		* 2450123.7 0.0 (JD method)
24232		* 2451545.0 -1421.3 (J2000 method)
24233		* 2400000.5 50123.2 (MJD method)
24234		* 2450123.5 0.2 (date & time method)
24235		*</pre>
24236		* The JD method is the most natural and convenient to use in
24237		* cases where the loss of several decimal digits of resolution
24238		* is acceptable. The J2000 method is best matched to the way
24239		* the argument is handled internally and will deliver the
24240		* optimum resolution. The MJD method and the date & time methods
24241		* are both good compromises between resolution and convenience.
24242		*
24243		* <li> The Celestial Intermediate Pole coordinates are the x,y
24244		* components of the unit vector in the Geocentric Celestial
24245		* Reference System.
24246		*
24247		* <li> The CIO locator s (in radians) positions the Celestial
24248		* Intermediate Origin on the equator of the CIP.
24249		*
24250		* <li> The present function is faster, but slightly less accurate (about
24251		* 1 mas in X,Y), than the jauXys00a function.
24252		*</ol>
24253		*<p>Called:<ul>
24254		* <li>{@link #jauPnm00b} classical NPB matrix, IAU 2000B
24255		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
24256		* <li>{@link #jauS00} the CIO locator s, given X,Y, IAU 2000A
24257		* </ul>
24258		*<p>Reference:
24259		*
24260		* <p>McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
24261		* IERS Technical Note No. 32, BKG (2004)
24262		*
24263		*@version 2008 May 12
24264		*
24265		* @since Release 20101201
24266		*
24267		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24268		*/
24269		public static ICRFrame jauXys00b(double date1, double date2)
24270		{
24271	2	double rbpn[][] = new double[3][3];
24272
24273
24274		/* Form the bias-precession-nutation matrix, IAU 2000A. */
24275	2	rbpn = jauPnm00b(date1, date2);
24276
24277		/* Extract X,Y. */
24278	2	CelestialIntermediatePole cip = jauBpn2xy(rbpn);
24279
24280		/* Obtain s. */
24281	2	double s = jauS00(date1, date2, cip.x, cip.y);
24282
24283	2	return new ICRFrame(cip, s);
24284
24285		}
24286
24287
24288		/**
24289		* For a given TT date, compute the X,Y coordinates of the Celestial
24290		* Intermediate Pole and the CIO locator s, using the IAU 2006
24291		* precession and IAU 2000A nutation models.
24292		*
24293		*<p>This function is derived from the International Astronomical Union's
24294		* SOFA (Standards Of Fundamental Astronomy) software collection.
24295		*
24296		*<p>Status: support function.
24297		*
24298		*<!-- Given: -->
24299		* @param date1 double TT as a 2-part Julian Date (Note 1)
24300		* @param date2 double TT as a 2-part Julian Date (Note 1)
24301		*
24302		*<!-- Returned: -->
24303		* @return x double <u>returned</u> Celestial Intermediate Pole (Note 2)
24304		* y double <u>returned</u> Celestial Intermediate Pole (Note 2)
24305		* s double <u>returned</u> the CIO locator s (Note 2)
24306		*
24307		* <p>Notes:
24308		* <ol>
24309		*
24310		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
24311		* convenient way between the two arguments. For example,
24312		* JD(TT)=2450123.7 could be expressed in any of these ways,
24313		* among others:
24314		*<pre>
24315		* date1 date2
24316		*
24317		* 2450123.7 0.0 (JD method)
24318		* 2451545.0 -1421.3 (J2000 method)
24319		* 2400000.5 50123.2 (MJD method)
24320		* 2450123.5 0.2 (date & time method)
24321		*</pre>
24322		* The JD method is the most natural and convenient to use in
24323		* cases where the loss of several decimal digits of resolution
24324		* is acceptable. The J2000 method is best matched to the way
24325		* the argument is handled internally and will deliver the
24326		* optimum resolution. The MJD method and the date & time methods
24327		* are both good compromises between resolution and convenience.
24328		*
24329		* <li> The Celestial Intermediate Pole coordinates are the x,y components
24330		* of the unit vector in the Geocentric Celestial Reference System.
24331		*
24332		* <li> The CIO locator s (in radians) positions the Celestial
24333		* Intermediate Origin on the equator of the CIP.
24334		*
24335		* <li> Series-based solutions for generating X and Y are also available:
24336		* see Capitaine & Wallace (2006) and jauXy06.
24337		*</ol>
24338		*<p>Called:<ul>
24339		* <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
24340		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
24341		* <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
24342		* </ul>
24343		*<p>References:
24344		*
24345		* <p>Capitaine, N. & Wallace, P.T., 2006, Astron.Astrophys. 450, 855
24346		*
24347		* <p>Wallace, P.T. & Capitaine, N., 2006, Astron.Astrophys. 459, 981
24348		*
24349		*@version 2008 May 11
24350		*
24351		* @since Release 20101201
24352		*
24353		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24354		*/
24355		public static ICRFrame jauXys06a(double date1, double date2)
24356		{
24357	2	double rbpn[][] = new double[3][3];
24358
24359
24360		/* Form the bias-precession-nutation matrix, IAU 2000A. */
24361	2	rbpn = jauPnm06a(date1, date2);
24362
24363		/* Extract X,Y. */
24364	2	CelestialIntermediatePole cip = jauBpn2xy(rbpn);
24365
24366		/* Obtain s. */
24367	2	double s = jauS06(date1, date2, cip.x, cip.y);
24368
24369	2	return new ICRFrame(cip, s);
24370
24371		}
24372
24373
24374		/**
24375		* Zero a p-vector.
24376		*
24377		*<p>This function is derived from the International Astronomical Union's
24378		* SOFA (Standards Of Fundamental Astronomy) software collection.
24379		*
24380		*<p>Status: vector/matrix support function.
24381		*
24382		*<!-- Returned: -->
24383		* @param p double[3] <u>returned</u> p-vector
24384		*
24385		*@version 2008 May 11
24386		*
24387		* @since Release 20101201
24388		*
24389		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24390		*/
24391		public static void jauZp(double p[] )
24392		{
24393	32	p[0] = 0.0;
24394	32	p[1] = 0.0;
24395	32	p[2] = 0.0;
24396
24397	32	return;
24398
24399		}
24400
24401
24402		/**
24403		* Zero a pv-vector.
24404		*
24405		*<p>This function is derived from the International Astronomical Union's
24406		* SOFA (Standards Of Fundamental Astronomy) software collection.
24407		*
24408		*<p>Status: vector/matrix support function.
24409		*
24410		*<!-- Returned: -->
24411		* @param pv double[2][3] <u>returned</u> pv-vector
24412		*
24413		*<p>Called:<ul>
24414		* <li>{@link #jauZp} zero p-vector
24415		* </ul>
24416		*@version 2008 May 11
24417		*
24418		* @since Release 20101201
24419		*
24420		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24421		*/
24422		public static void jauZpv(double pv[][])
24423		{
24424	2	jauZp(pv[0]);
24425	2	jauZp(pv[1]);
24426
24427	2	return;
24428
24429		}
24430
24431
24432		/**
24433		* Initialize an r-matrix to the null matrix.
24434		*
24435		*<p>This function is derived from the International Astronomical Union's
24436		* SOFA (Standards Of Fundamental Astronomy) software collection.
24437		*
24438		*<p>Status: vector/matrix support function.
24439		*
24440		*<!-- Returned: -->
24441		* @param r double[3][3] <u>returned</u> r-matrix
24442		*
24443		*@version 2008 May 11
24444		*
24445		* @since Release 20101201
24446		*
24447		* <!-- Copyright (C) 2009 IAU SOFA Review Board. See notes at end -->
24448		*/
24449		public static void jauZr(double r[][])
24450		{
24451		int i, j;
24452
24453
24454	5216	for (i = 0; i < 3; i++) {
24455	15648	for (j = 0; j < 3; j++) {
24456	11736	r[i][j] = 0.0;
24457		}
24458		}
24459
24460	1304	return;
24461
24462		}
24463
24464
24465		/**
24466		* returns the first argument modulo the second.
24467		* Utility function to retain C use of fmod.
24468		* @param d
24469		* @param d2
24470		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 27 Jan 2010
24471		* @return
24472		*/
24473		private static double fmod(double d, double d2) {
24474	97158	return d % d2;
24475		}
24476		//IMPL new 20131202 routines after here
24477
24478		/**
24479		* Star-independent astrometry parameters.
24480		*
24481		* (Vectors eb, eh, em and v are all with respect to BCRS axes.)
24482		*
24483		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 26 Mar 2014
24484		* @since 20131202
24485		*/
24486		public static class Astrom {
24487
24488		/** PM time interval (SSB, Julian years) */
24489		public double pmt;
24490		/** SSB to observer (vector, au) [3]*/
24491	58	public double eb[] = new double[3];
24492		/** Sun to observer (unit vector)[3] */
24493	58	public double eh[] = new double[3];
24494		/** distance from Sun to observer (au) */
24495		public double em;
24496		/** barycentric observer velocity (vector, c)[3] */
24497	58	public double v[] = new double[3];
24498		/** sqrt(1-\|v\|^2): reciprocal of Lorenz factor */
24499		public double bm1;
24500		/** bias-precession-nutation matrix [3][3] */
24501	58	public double bpn[][] = new double[3][3];
24502		/** longitude + s' + dERA(DUT) (radians) */
24503		public double along;
24504		/** geodetic latitude (radians) */
24505		public double phi;
24506		/** polar motion xp wrt local meridian (radians) */
24507		public double xpl;
24508		/** polar motion yp wrt local meridian (radians) */
24509		public double ypl;
24510		/** sine of geodetic latitude */
24511		public double sphi;
24512		/** cosine of geodetic latitude */
24513		public double cphi;
24514		/** magnitude of diurnal aberration vector */
24515		public double diurab;
24516		/** "local" Earth rotation angle (radians) */
24517		public double eral;
24518		/** refraction constant A (radians) */
24519		public double refa;
24520		/** refraction constant B (radians) */
24521		public double refb;
24522
24523		/**
24524		*
24525		*/
24526	116	public Astrom(){}
24527		} ;
24528
24529		/**
24530		* Body parameters for light deflection.
24531		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 26 Mar 2014
24532		* @since 20131202
24533		*/
24534	18	public static class Ldbody {
24535		/** mass of the body (solar masses) */
24536		public double bm;
24537		/** deflection limiter (radians^2/2) */
24538		public double dl;
24539		/** barycentric PV of the body (au, au/day)[2][3] */
24540	18	public double pv[][] = new double [2][3];
24541		} ;
24542
24543
24544		/**
24545		* Apply aberration to transform natural direction into proper
24546		* direction.
24547		*
24548		*<p>This function is derived from the International Astronomical Union's
24549		* SOFA (Standards of Fundamental Astronomy) software collection.
24550		*
24551		*<p>Status: support function.
24552		*
24553		*<!-- Given: -->
24554		* @param pnat double[3] natural direction to the source (unit vector)
24555		* @param v double[3] observer barycentric velocity in units of c
24556		* @param s double distance between the Sun and the observer (au)
24557		* @param bm1 double sqrt(1-\|v\|^2): reciprocal of Lorenz factor
24558		*
24559		*<!-- Returned:-->
24560		* @return ppr double[3] <b>Returned</b> proper direction to source (unit vector)
24561		*
24562		*<p>Notes:
24563		* <ol>
24564		*
24565		* <li> The algorithm is based on Expr. (7.40) in the Explanatory
24566		* Supplement (Urban & Seidelmann 2013), but with the following
24567		* changes:
24568		*
24569		* <p>o Rigorous rather than approximate normalization is applied.
24570		*
24571		* <p>o The gravitational potential term from Expr. (7) in
24572		* Klioner (2003) is added, taking into account only the Sun's
24573		* contribution. This has a maximum effect of about
24574		* 0.4 microarcsecond.
24575		*
24576		* <li> In almost all cases, the maximum accuracy will be limited by the
24577		* supplied velocity. For example, if the SOFA iauEpv00 function is
24578		* used, errors of up to 5 microarcseconds could occur.
24579		*
24580		* </ol>
24581		*<p>References:
24582		* <ul>
24583		*
24584		* <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
24585		* the Astronomical Almanac, 3rd ed., University Science Books
24586		* (2013).
24587		*
24588		* <li> Klioner, Sergei A., "A practical relativistic model for micro-
24589		* arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
24590		*
24591		* </ul>
24592		* Called:
24593		* <ul>
24594		* <li>{@link #jauPdp} scalar product of two p-vectors
24595		*
24596		* </ul>
24597		*@version 2013 October 9
24598		*
24599		*@since JSOFA release 20131202
24600		*
24601		*
24602		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24603		*/
24604		public static double[] jauAb(double pnat[], double v[], double s, double bm1
24605		)
24606		{
24607		int i;
24608	36	double pdv, w1, w2, r2, w, p[] = new double[3], r;
24609	36	double ppr[] = new double[3];
24610
24611	36	pdv = jauPdp(pnat, v);
24612	36	w1 = 1.0 + pdv/(1.0 + bm1);
24613	36	w2 = SRS/s;
24614	36	r2 = 0.0;
24615	144	for (i = 0; i < 3; i++) {
24616	108	w = pnat[i]bm1 + w1v[i] + w2(v[i] - pdvpnat[i]);
24617	108	p[i] = w;
24618	108	r2 = r2 + w*w;
24619		}
24620	36	r = sqrt(r2);
24621	144	for (i = 0; i < 3; i++) {
24622	108	ppr[i] = p[i]/r;
24623		}
24624	36	return ppr;
24625		/* Finished. */
24626
24627
24628		}
24629
24630		/**
24631		* For a geocentric observer, prepare star-independent astrometry
24632		* parameters for transformations between ICRS and GCRS coordinates.
24633		* The Earth ephemeris is supplied by the caller.
24634		*
24635		* The parameters produced by this function are required in the
24636		* parallax, light deflection and aberration parts of the astrometric
24637		* transformation chain.
24638		*
24639		*<p>This function is derived from the International Astronomical Union's
24640		* SOFA (Standards of Fundamental Astronomy) software collection.
24641		*
24642		*<p>Status: support function.
24643		*
24644		*<!-- Given: -->
24645		* @param date1 double TDB as a 2-part...
24646		* @param date2 double ...Julian Date (Note 1)
24647		* @param ebpv double[2][3] Earth barycentric pos/vel (au, au/day)
24648		* @param ehp double[3] Earth heliocentric position (au)
24649		*
24650		*<!-- Returned:-->
24651		* @param astrom jauASTROM <b>Returned</b> star-independent astrometry parameters:
24652		*
24653		*<p>Notes:
24654		* <ol>
24655		*
24656		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
24657		* convenient way between the two arguments. For example,
24658		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
24659		* others:
24660		* <pre>
24661		* date1 date2
24662		*
24663		* 2450123.7 0.0 (JD method)
24664		* 2451545.0 -1421.3 (J2000 method)
24665		* 2400000.5 50123.2 (MJD method)
24666		* 2450123.5 0.2 (date & time method)
24667		* </pre>
24668		* <p>The JD method is the most natural and convenient to use in cases
24669		* where the loss of several decimal digits of resolution is
24670		* acceptable. The J2000 method is best matched to the way the
24671		* argument is handled internally and will deliver the optimum
24672		* resolution. The MJD method and the date & time methods are both
24673		* good compromises between resolution and convenience. For most
24674		* applications of this function the choice will not be at all
24675		* critical.
24676		*
24677		* <p>TT can be used instead of TDB without any significant impact on
24678		* accuracy.
24679		*
24680		* <li> All the vectors are with respect to BCRS axes.
24681		*
24682		* <li> This is one of several functions that inserts into the astrom
24683		* structure star-independent parameters needed for the chain of
24684		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed}.
24685		*
24686		* <p>The various functions support different classes of observer and
24687		* portions of the transformation chain:
24688		* <pre>{@literal
24689		* functions observer transformation
24690		*
24691		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
24692		* iauApci iauApci13 terrestrial ICRS <-> CIRS
24693		* iauApco iauApco13 terrestrial ICRS <-> observed
24694		* iauApcs iauApcs13 space ICRS <-> GCRS
24695		* iauAper iauAper13 terrestrial update Earth rotation
24696		* iauApio iauApio13 terrestrial CIRS <-> observed
24697		* }</pre>
24698		*
24699		* <p>Those with names ending in "13" use contemporary SOFA models to
24700		* compute the various ephemerides. The others accept ephemerides
24701		* supplied by the caller.
24702		*
24703		* <p>The transformation from ICRS to GCRS covers space motion,
24704		* parallax, light deflection, and aberration. From GCRS to CIRS
24705		* comprises frame bias and precession-nutation. From CIRS to
24706		* observed takes account of Earth rotation, polar motion, diurnal
24707		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
24708		* transformation), and atmospheric refraction.
24709		*
24710		* <li> The context structure astrom produced by this function is used by
24711		* iauAtciq* and iauAticq*.
24712		*
24713		* </ol>
24714		* Called:
24715		* <ul>
24716		* <li>{@link #jauApcs} astrometry parameters, ICRS-GCRS, space observer
24717		*
24718		* </ul>
24719		*@version 2013 October 9
24720		*
24721		*@since JSOFA release 20131202
24722		*
24723		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24724		*/
24725		public static void jauApcg(double date1, double date2,
24726		double ebpv[][], double ehp[],
24727		Astrom astrom)
24728		{
24729		/* Geocentric observer */
24730	22	double pv[][] = { { 0.0, 0.0, 0.0 },
24731		{ 0.0, 0.0, 0.0 } };
24732
24733
24734		/* Compute the star-independent astrometry parameters. */
24735	22	jauApcs(date1, date2, pv, ebpv, ehp, astrom);
24736
24737		/* Finished. */
24738
24739
24740	22	}
24741
24742		/**
24743		* For a geocentric observer, prepare star-independent astrometry
24744		* parameters for transformations between ICRS and GCRS coordinates.
24745		* The caller supplies the date, and SOFA models are used to predict
24746		* the Earth ephemeris.
24747		*
24748		* The parameters produced by this function are required in the
24749		* parallax, light deflection and aberration parts of the astrometric
24750		* transformation chain.
24751		*
24752		*<p>This function is derived from the International Astronomical Union's
24753		* SOFA (Standards of Fundamental Astronomy) software collection.
24754		*
24755		*<p>Status: support function.
24756		*
24757		*<!-- Given: -->
24758		* @param date1 double TDB as a 2-part...
24759		* @param date2 double ...Julian Date (Note 1)
24760		*
24761		*<!-- Returned:-->
24762		* @param astrom <b>Returned</b> star-independent astrometry parameters:
24763		*
24764		*<p>Notes:
24765		* <ol>
24766		*
24767		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
24768		* convenient way between the two arguments. For example,
24769		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
24770		* others:
24771		* <pre>
24772		* date1 date2
24773		*
24774		* 2450123.7 0.0 (JD method)
24775		* 2451545.0 -1421.3 (J2000 method)
24776		* 2400000.5 50123.2 (MJD method)
24777		* 2450123.5 0.2 (date & time method)
24778		* </pre>
24779		* <p>The JD method is the most natural and convenient to use in cases
24780		* where the loss of several decimal digits of resolution is
24781		* acceptable. The J2000 method is best matched to the way the
24782		* argument is handled internally and will deliver the optimum
24783		* resolution. The MJD method and the date & time methods are both
24784		* good compromises between resolution and convenience. For most
24785		* applications of this function the choice will not be at all
24786		* critical.
24787		*
24788		* <p>TT can be used instead of TDB without any significant impact on
24789		* accuracy.
24790		*
24791		* <li> All the vectors are with respect to BCRS axes.
24792		*
24793		* <li> In cases where the caller wishes to supply his own Earth
24794		* ephemeris, the function iauApcg can be used instead of the present
24795		* function.
24796		*
24797		* <li> This is one of several functions that inserts into the astrom
24798		* structure star-independent parameters needed for the chain of
24799		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed}.
24800		*
24801		* <p>The various functions support different classes of observer and
24802		* portions of the transformation chain:
24803		* <pre>
24804		* {@literal
24805		* functions observer transformation
24806		*
24807		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
24808		* iauApci iauApci13 terrestrial ICRS <-> CIRS
24809		* iauApco iauApco13 terrestrial ICRS <-> observed
24810		* iauApcs iauApcs13 space ICRS <-> GCRS
24811		* iauAper iauAper13 terrestrial update Earth rotation
24812		* iauApio iauApio13 terrestrial CIRS <-> observed
24813		* }
24814		* </pre>
24815		* <p>Those with names ending in "13" use contemporary SOFA models to
24816		* compute the various ephemerides. The others accept ephemerides
24817		* supplied by the caller.
24818		*
24819		* <p>The transformation from ICRS to GCRS covers space motion,
24820		* parallax, light deflection, and aberration. From GCRS to CIRS
24821		* comprises frame bias and precession-nutation. From CIRS to
24822		* observed takes account of Earth rotation, polar motion, diurnal
24823		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
24824		* transformation), and atmospheric refraction.
24825		*
24826		* <li> The context structure astrom produced by this function is used by
24827		* iauAtciq* and iauAticq*.
24828		*
24829		* </ol>
24830		* Called:
24831		* <ul>
24832		* <li>{@link #jauEpv00} Earth position and velocity
24833		* <li>{@link #jauApcg} astrometry parameters, ICRS-GCRS, geocenter
24834		*
24835		* </ul>
24836		*@version 2013 October 9
24837		*
24838		*@since JSOFA release 20131202
24839		*
24840		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24841		*/
24842		public static void jauApcg13(double date1, double date2, Astrom astrom)
24843		{
24844	2	double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3];
24845
24846
24847		/* Earth barycentric & heliocentric position/velocity (au, au/d). */
24848	2	jauEpv00(date1, date2, ehpv, ebpv);
24849
24850		/* Compute the star-independent astrometry parameters. */
24851	2	jauApcg(date1, date2, ebpv, ehpv[0], astrom);
24852
24853		/* Finished. */
24854
24855
24856	2	}
24857
24858		/**
24859		* For a terrestrial observer, prepare star-independent astrometry
24860		* parameters for transformations between ICRS and geocentric CIRS
24861		* coordinates. The Earth ephemeris and CIP/CIO are supplied by the
24862		* caller.
24863		*
24864		* The parameters produced by this function are required in the
24865		* parallax, light deflection, aberration, and bias-precession-nutation
24866		* parts of the astrometric transformation chain.
24867		*
24868		*<p>This function is derived from the International Astronomical Union's
24869		* SOFA (Standards of Fundamental Astronomy) software collection.
24870		*
24871		*<p>Status: support function.
24872		*
24873		*<!-- Given: -->
24874		* @param date1 double TDB as a 2-part...
24875		* @param date2 double ...Julian Date (Note 1)
24876		* @param ebpv double[2][3] Earth barycentric position/velocity (au, au/day)
24877		* @param ehp double[3] Earth heliocentric position (au)
24878		* @param x double CIP X,Y (components of unit vector)
24879		* @param y double CIP X,Y (components of unit vector)
24880		* @param s double the CIO locator s (radians)
24881		*
24882		*<!-- Returned:-->
24883		* @param astrom <b>Returned</b> star-independent astrometry parameters:
24884		*
24885		*<p>Notes:
24886		* <ol>
24887		*
24888		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
24889		* convenient way between the two arguments. For example,
24890		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
24891		* others:
24892		* <pre>
24893		* date1 date2
24894		*
24895		* 2450123.7 0.0 (JD method)
24896		* 2451545.0 -1421.3 (J2000 method)
24897		* 2400000.5 50123.2 (MJD method)
24898		* 2450123.5 0.2 (date & time method)
24899		* </pre>
24900		* <p>The JD method is the most natural and convenient to use in cases
24901		* where the loss of several decimal digits of resolution is
24902		* acceptable. The J2000 method is best matched to the way the
24903		* argument is handled internally and will deliver the optimum
24904		* resolution. The MJD method and the date & time methods are both
24905		* good compromises between resolution and convenience. For most
24906		* applications of this function the choice will not be at all
24907		* critical.
24908		*
24909		* <p>TT can be used instead of TDB without any significant impact on
24910		* accuracy.
24911		*
24912		* <li> All the vectors are with respect to BCRS axes.
24913		*
24914		* <li> In cases where the caller does not wish to provide the Earth
24915		* ephemeris and CIP/CIO, the function iauApci13 can be used instead
24916		* of the present function. This computes the required quantities
24917		* using other SOFA functions.
24918		*
24919		* <li> This is one of several functions that inserts into the astrom
24920		* structure star-independent parameters needed for the chain of
24921		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
24922		*
24923		* <p>The various functions support different classes of observer and
24924		* portions of the transformation chain:
24925		* <pre>{@literal
24926		* functions observer transformation
24927		*
24928		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
24929		* iauApci iauApci13 terrestrial ICRS <-> CIRS
24930		* iauApco iauApco13 terrestrial ICRS <-> observed
24931		* iauApcs iauApcs13 space ICRS <-> GCRS
24932		* iauAper iauAper13 terrestrial update Earth rotation
24933		* iauApio iauApio13 terrestrial CIRS <-> observed
24934		* }</pre>
24935		* <p>Those with names ending in "13" use contemporary SOFA models to
24936		* compute the various ephemerides. The others accept ephemerides
24937		* supplied by the caller.
24938		*
24939		* <p>The transformation from ICRS to GCRS covers space motion,
24940		* parallax, light deflection, and aberration. From GCRS to CIRS
24941		* comprises frame bias and precession-nutation. From CIRS to
24942		* observed takes account of Earth rotation, polar motion, diurnal
24943		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
24944		* transformation), and atmospheric refraction.
24945		*
24946		* <li> The context structure astrom produced by this function is used by
24947		* iauAtciq* and iauAticq*.
24948		*
24949		* </ol>
24950		* Called:
24951		* <ul>
24952		* <li>{@link #jauApcg} astrometry parameters, ICRS-GCRS, geocenter
24953		* <li>{@link #jauC2ixys} celestial-to-intermediate matrix, given X,Y and s
24954		*
24955		* </ul>
24956		*@version 2013 September 25
24957		*
24958		*@since JSOFA release 20131202
24959		*
24960		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
24961		*/
24962		public static void jauApci(double date1, double date2,
24963		double ebpv[][], double ehp[],
24964		double x, double y, double s,
24965		Astrom astrom)
24966		{
24967
24968		/* Star-independent astrometry parameters for geocenter. */
24969	18	jauApcg(date1, date2, ebpv, ehp, astrom);
24970
24971		/* CIO based BPN matrix. */
24972	18	astrom.bpn = jauC2ixys(x, y, s);
24973
24974		/* Finished. */
24975
24976
24977	18	}
24978
24979		/**
24980		* For a terrestrial observer, prepare star-independent astrometry
24981		* parameters for transformations between ICRS and geocentric CIRS
24982		* coordinates. The caller supplies the date, and SOFA models are used
24983		* to predict the Earth ephemeris and CIP/CIO.
24984		*
24985		* The parameters produced by this function are required in the
24986		* parallax, light deflection, aberration, and bias-precession-nutation
24987		* parts of the astrometric transformation chain.
24988		*
24989		*<p>This function is derived from the International Astronomical Union's
24990		* SOFA (Standards of Fundamental Astronomy) software collection.
24991		*
24992		*<p>Status: support function.
24993		*
24994		*<!-- Given: -->
24995		* @param date1 double TDB as a 2-part...
24996		* @param date2 double ...Julian Date (Note 1)
24997		*
24998		*<!-- Returned:-->
24999		* @param astrom jauASTROM <b>Returned</b> star-independent astrometry parameters:
25000		* pmt double <b>Returned</b> PM time interval (SSB, Julian years)
25001		* eb double[3] <b>Returned</b> SSB to observer (vector, au)
25002		* eh double[3] <b>Returned</b> Sun to observer (unit vector)
25003		* em double <b>Returned</b> distance from Sun to observer (au)
25004		* v double[3] <b>Returned</b> barycentric observer velocity (vector, c)
25005		* bm1 double <b>Returned</b> sqrt(1-\|v\|^2): reciprocal of Lorenz factor
25006		* bpn double[3][3] <b>Returned</b> bias-precession-nutation matrix
25007		* along double <b>Returned</b> unchanged
25008		* xpl double <b>Returned</b> unchanged
25009		* ypl double <b>Returned</b> unchanged
25010		* sphi double <b>Returned</b> unchanged
25011		* cphi double <b>Returned</b> unchanged
25012		* diurab double <b>Returned</b> unchanged
25013		* eral double <b>Returned</b> unchanged
25014		* refa double <b>Returned</b> unchanged
25015		* refb double <b>Returned</b> unchanged
25016		* @return double* <b>Returned</b> equation of the origins (ERA-GST)
25017		*
25018		*<p>Notes:
25019		* <ol>
25020		*
25021		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25022		* convenient way between the two arguments. For example,
25023		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
25024		* others:
25025		* <pre>
25026		* date1 date2
25027		*
25028		* 2450123.7 0.0 (JD method)
25029		* 2451545.0 -1421.3 (J2000 method)
25030		* 2400000.5 50123.2 (MJD method)
25031		* 2450123.5 0.2 (date & time method)
25032		* </pre>
25033		* <p>The JD method is the most natural and convenient to use in cases
25034		* where the loss of several decimal digits of resolution is
25035		* acceptable. The J2000 method is best matched to the way the
25036		* argument is handled internally and will deliver the optimum
25037		* resolution. The MJD method and the date & time methods are both
25038		* good compromises between resolution and convenience. For most
25039		* applications of this function the choice will not be at all
25040		* critical.
25041		*
25042		* <p>TT can be used instead of TDB without any significant impact on
25043		* accuracy.
25044		*
25045		* <li> All the vectors are with respect to BCRS axes.
25046		*
25047		* <li> In cases where the caller wishes to supply his own Earth
25048		* ephemeris and CIP/CIO, the function iauApci can be used instead
25049		* of the present function.
25050		*
25051		* <li> This is one of several functions that inserts into the astrom
25052		* structure star-independent parameters needed for the chain of
25053		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25054		*
25055		* <p>The various functions support different classes of observer and
25056		* portions of the transformation chain:
25057		* <pre>{@literal
25058		* functions observer transformation
25059		*
25060		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
25061		* iauApci iauApci13 terrestrial ICRS <-> CIRS
25062		* iauApco iauApco13 terrestrial ICRS <-> observed
25063		* iauApcs iauApcs13 space ICRS <-> GCRS
25064		* iauAper iauAper13 terrestrial update Earth rotation
25065		* iauApio iauApio13 terrestrial CIRS <-> observed
25066		* }</pre>
25067		* <p>Those with names ending in "13" use contemporary SOFA models to
25068		* compute the various ephemerides. The others accept ephemerides
25069		* supplied by the caller.
25070		*
25071		* <p>The transformation from ICRS to GCRS covers space motion,
25072		* parallax, light deflection, and aberration. From GCRS to CIRS
25073		* comprises frame bias and precession-nutation. From CIRS to
25074		* observed takes account of Earth rotation, polar motion, diurnal
25075		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25076		* transformation), and atmospheric refraction.
25077		*
25078		* <li> The context structure astrom produced by this function is used by
25079		* iauAtciq* and iauAticq*.
25080		*
25081		* </ol>
25082		* Called:
25083		* <ul>
25084		* <li>{@link #jauEpv00} Earth position and velocity
25085		* <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
25086		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
25087		* <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
25088		* <li>{@link #jauApci} astrometry parameters, ICRS-CIRS
25089		* <li>{@link #jauEors} equation of the origins, given NPB matrix and s
25090		*
25091		* </ul>
25092		*@version 2013 October 9
25093		*
25094		*@since JSOFA release 20131202
25095		*
25096		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25097		*/
25098		public static double jauApci13(double date1, double date2,
25099		Astrom astrom)
25100		{
25101	16	double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3], r[][], s;
25102
25103
25104		/* Earth barycentric & heliocentric position/velocity (au, au/d). */
25105	16	jauEpv00(date1, date2, ehpv, ebpv);
25106
25107		/* Form the equinox based BPN matrix, IAU 2006/2000A. */
25108	16	r = jauPnm06a(date1, date2);
25109
25110		/* Extract CIP X,Y. */
25111	16	CelestialIntermediatePole cip = jauBpn2xy(r);
25112
25113		/* Obtain CIO locator s. */
25114	16	s = jauS06(date1, date2, cip.x, cip.y);
25115
25116		/* Compute the star-independent astrometry parameters. */
25117	16	jauApci(date1, date2, ebpv, ehpv[0], cip.x, cip.y, s, astrom);
25118
25119		/* Equation of the origins. */
25120	16	return jauEors(r, s);
25121
25122		/* Finished. */
25123
25124
25125		}
25126
25127		/**
25128		* For a terrestrial observer, prepare star-independent astrometry
25129		* parameters for transformations between ICRS and observed
25130		* coordinates. The caller supplies the Earth ephemeris, the Earth
25131		* rotation information and the refraction constants as well as the
25132		* site coordinates.
25133		*
25134		*<p>This function is derived from the International Astronomical Union's
25135		* SOFA (Standards of Fundamental Astronomy) software collection.
25136		*
25137		*<p>Status: support function.
25138		*
25139		*<!-- Given: -->
25140		* @param date1 double TDB as a 2-part...
25141		* @param date2 double ...Julian Date (Note 1)
25142		* @param ebpv double[2][3] Earth barycentric PV (au, au/day, Note 2)
25143		* @param ehp double[3] Earth heliocentric P (au, Note 2)
25144		* @param x double CIP X,Y (components of unit vector)
25145		* @param y double CIP X,Y (components of unit vector)
25146		* @param s double the CIO locator s (radians)
25147		* @param theta double Earth rotation angle (radians)
25148		* @param elong double longitude (radians, east +ve, Note 3)
25149		* @param phi double latitude (geodetic, radians, Note 3)
25150		* @param hm double height above ellipsoid (m, geodetic, Note 3)
25151		* @param xp double polar motion coordinates (radians, Note 4)
25152		* @param yp double polar motion coordinates (radians, Note 4)
25153		* @param sp double the TIO locator s' (radians, Note 4)
25154		* @param refa double refraction constant A (radians, Note 5)
25155		* @param refb double refraction constant B (radians, Note 5)
25156		*
25157		*<!-- Returned:-->
25158		* @param astrom <b>Returned</b> star-independent astrometry parameters:
25159		*
25160		*<p>Notes:
25161		* <ol>
25162		*
25163		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25164		* convenient way between the two arguments. For example,
25165		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
25166		* others:
25167		* <pre>
25168		* date1 date2
25169		*
25170		* 2450123.7 0.0 (JD method)
25171		* 2451545.0 -1421.3 (J2000 method)
25172		* 2400000.5 50123.2 (MJD method)
25173		* 2450123.5 0.2 (date & time method)
25174		* </pre>
25175		* <p>The JD method is the most natural and convenient to use in cases
25176		* where the loss of several decimal digits of resolution is
25177		* acceptable. The J2000 method is best matched to the way the
25178		* argument is handled internally and will deliver the optimum
25179		* resolution. The MJD method and the date & time methods are both
25180		* good compromises between resolution and convenience. For most
25181		* applications of this function the choice will not be at all
25182		* critical.
25183		*
25184		* <p>TT can be used instead of TDB without any significant impact on
25185		* accuracy.
25186		*
25187		* <li> The vectors eb, eh, and all the astrom vectors, are with respect
25188		* to BCRS axes.
25189		*
25190		* <li> The geographical coordinates are with respect to the WGS84
25191		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN
25192		* CONVENTION: the longitude required by the present function is
25193		* right-handed, i.e. east-positive, in accordance with geographical
25194		* convention.
25195		*
25196		* <li> xp and yp are the coordinates (in radians) of the Celestial
25197		* Intermediate Pole with respect to the International Terrestrial
25198		* Reference System (see IERS Conventions), measured along the
25199		* meridians 0 and 90 deg west respectively. sp is the TIO locator
25200		* s', in radians, which positions the Terrestrial Intermediate
25201		* Origin on the equator. For many applications, xp, yp and
25202		* (especially) sp can be set to zero.
25203		*
25204		* <p>Internally, the polar motion is stored in a form rotated onto the
25205		* local meridian.
25206		*
25207		* <li> The refraction constants refa and refb are for use in a
25208		* dZ = Atan(Z)+Btan^3(Z) model, where Z is the observed
25209		* (i.e. refracted) zenith distance and dZ is the amount of
25210		* refraction.
25211		*
25212		* <li> It is advisable to take great care with units, as even unlikely
25213		* values of the input parameters are accepted and processed in
25214		* accordance with the models used.
25215		*
25216		* <li> In cases where the caller does not wish to provide the Earth
25217		* Ephemeris, the Earth rotation information and refraction
25218		* constants, the function iauApco13 can be used instead of the
25219		* present function. This starts from UTC and weather readings etc.
25220		* and computes suitable values using other SOFA functions.
25221		*
25222		* <li> This is one of several functions that inserts into the astrom
25223		* structure star-independent parameters needed for the chain of
25224		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25225		*
25226		* <p>The various functions support different classes of observer and
25227		* portions of the transformation chain:
25228		* <pre>{@literal
25229		* functions observer transformation
25230		*
25231		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
25232		* iauApci iauApci13 terrestrial ICRS <-> CIRS
25233		* iauApco iauApco13 terrestrial ICRS <-> observed
25234		* iauApcs iauApcs13 space ICRS <-> GCRS
25235		* iauAper iauAper13 terrestrial update Earth rotation
25236		* iauApio iauApio13 terrestrial CIRS <-> observed
25237		* }</pre>
25238		* <p>Those with names ending in "13" use contemporary SOFA models to
25239		* compute the various ephemerides. The others accept ephemerides
25240		* supplied by the caller.
25241		*
25242		* <p>The transformation from ICRS to GCRS covers space motion,
25243		* parallax, light deflection, and aberration. From GCRS to CIRS
25244		* comprises frame bias and precession-nutation. From CIRS to
25245		* observed takes account of Earth rotation, polar motion, diurnal
25246		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25247		* transformation), and atmospheric refraction.
25248		*
25249		* <li> The context structure astrom produced by this function is used by
25250		* iauAtioq, iauAtoiq, iauAtciq* and iauAticq*.
25251		*
25252		* </ol>
25253		* Called:
25254		* <ul>
25255		* <li>{@link #jauAper} astrometry parameters: update ERA
25256		* <li>{@link #jauC2ixys} celestial-to-intermediate matrix, given X,Y and s
25257		* <li>{@link #jauPvtob} position/velocity of terrestrial station
25258		* <li>{@link #jauTrxpv} product of transpose of r-matrix and pv-vector
25259		* <li>{@link #jauApcs} astrometry parameters, ICRS-GCRS, space observer
25260		* <li>{@link #jauCr} copy r-matrix
25261		*
25262		* </ul>
25263		*@version 2013 October 9
25264		*
25265		*@since JSOFA release 20131202
25266		*
25267		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25268		* @throws JSOFAInternalError
25269		* @throws JSOFAIllegalParameter
25270		*/
25271		public static void jauApco(double date1, double date2,
25272		double ebpv[][], double ehp[],
25273		double x, double y, double s, double theta,
25274		double elong, double phi, double hm,
25275		double xp, double yp, double sp,
25276		double refa, double refb,
25277		Astrom astrom) throws JSOFAIllegalParameter, JSOFAInternalError
25278		{
25279		double sl, cl, r[][], pvc[][], pv[][];
25280
25281
25282		/* Longitude with adjustment for TIO locator s'. */
25283	12	astrom.along = elong + sp;
25284
25285		/* Polar motion, rotated onto the local meridian. */
25286	12	sl = sin(astrom.along);
25287	12	cl = cos(astrom.along);
25288	12	astrom.xpl = xpcl - ypsl;
25289	12	astrom.ypl = xpsl + ypcl;
25290
25291		/* Functions of latitude. */
25292	12	astrom.sphi = sin(phi);
25293	12	astrom.cphi = cos(phi);
25294
25295		/* Refraction constants. */
25296	12	astrom.refa = refa;
25297	12	astrom.refb = refb;
25298
25299		/* Local Earth rotation angle. */
25300	12	jauAper(theta, astrom);
25301
25302		/* Disable the (redundant) diurnal aberration step. */
25303	12	astrom.diurab = 0.0;
25304
25305		/* CIO based BPN matrix. */
25306	12	r = jauC2ixys(x, y, s);
25307
25308		/* Observer's geocentric position and velocity (m, m/s, CIRS). */
25309	12	pvc = jauPvtob(elong, phi, hm, xp, yp, sp, theta);
25310
25311		/* Rotate into GCRS. */
25312	12	pv = jauTrxpv(r, pvc);
25313
25314		/* ICRS <-> GCRS parameters. */
25315	12	jauApcs(date1, date2, pv, ebpv, ehp, astrom);
25316
25317		/* Store the CIO based BPN matrix. */
25318	12	jauCr(r, astrom.bpn );
25319
25320		/* Finished. */
25321
25322
25323	12	}
25324
25325		/**
25326		* For a terrestrial observer, prepare star-independent astrometry
25327		* parameters for transformations between ICRS and observed
25328		* coordinates. The caller supplies UTC, site coordinates, ambient air
25329		* conditions and observing wavelength, and SOFA models are used to
25330		* obtain the Earth ephemeris, CIP/CIO and refraction constants.
25331		*
25332		* The parameters produced by this function are required in the
25333		* parallax, light deflection, aberration, and bias-precession-nutation
25334		* parts of the ICRS/CIRS transformations.
25335		*
25336		*<p>This function is derived from the International Astronomical Union's
25337		* SOFA (Standards of Fundamental Astronomy) software collection.
25338		*
25339		*<p>Status: support function.
25340		*
25341		*<!-- Given: -->
25342		* @param utc1 double UTC as a 2-part...
25343		* @param utc2 double ...quasi Julian Date (Notes 1,2)
25344		* @param dut1 double UT1-UTC (seconds, Note 3)
25345		* @param elong double longitude (radians, east +ve, Note 4)
25346		* @param phi double latitude (geodetic, radians, Note 4)
25347		* @param hm double height above ellipsoid (m, geodetic, Notes 4,6)
25348		* @param xp double polar motion coordinates (radians, Note 5)
25349		* @param yp double polar motion coordinates (radians, Note 5)
25350		* @param phpa double pressure at the observer (hPa = mB, Note 6)
25351		* @param tc double ambient temperature at the observer (deg C)
25352		* @param rh double relative humidity at the observer (range 0-1)
25353		* @param wl double wavelength (micrometers, Note 7)
25354		*
25355		*<!-- Returned:-->
25356		* @param astrom <b>Returned</b> star-independent astrometry parameters:
25357		*
25358		*
25359		* @return double <b>Returned</b> equation of the origins (ERA-GST)
25360		*
25361		* @throws JSOFAInternalError
25362		* @throws JSOFAIllegalParameter
25363		* int status: <b>Returned</b> +1 = dubious year (Note 2)
25364		* 0 = <b>Returned</b> OK
25365		* -1 = <b>Returned</b> unacceptable date
25366		*
25367		*<p>Notes:
25368		* <ol>
25369		*
25370		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
25371		* convenient way between the two arguments, for example where utc1
25372		* is the Julian Day Number and utc2 is the fraction of a day.
25373		*
25374		* <p>However, JD cannot unambiguously represent UTC during a leap
25375		* second unless special measures are taken. The convention in the
25376		* present function is that the JD day represents UTC days whether
25377		* the length is 86399, 86400 or 86401 SI seconds.
25378		*
25379		* <p>Applications should use the function iauDtf2d to convert from
25380		* calendar date and time of day into 2-part quasi Julian Date, as
25381		* it implements the leap-second-ambiguity convention just
25382		* described.
25383		*
25384		* <li> The warning status "dubious year" flags UTCs that predate the
25385		* introduction of the time scale or that are too far in the
25386		* future to be trusted. See iauDat for further details.
25387		*
25388		* <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
25389		* one second at the end of each positive UTC leap second,
25390		* introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
25391		* practice is under review, and in the future UT1-UTC may grow
25392		* essentially without limit.
25393		*
25394		* <li> The geographical coordinates are with respect to the WGS84
25395		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
25396		* longitude required by the present function is east-positive
25397		* (i.e. right-handed), in accordance with geographical convention.
25398		*
25399		* <li> The polar motion xp,yp can be obtained from IERS bulletins. The
25400		* values are the coordinates (in radians) of the Celestial
25401		* Intermediate Pole with respect to the International Terrestrial
25402		* Reference System (see IERS Conventions 2003), measured along the
25403		* meridians 0 and 90 deg west respectively. For many
25404		* applications, xp and yp can be set to zero.
25405		*
25406		* <p>Internally, the polar motion is stored in a form rotated onto
25407		* the local meridian.
25408		*
25409		* <li> If hm, the height above the ellipsoid of the observing station
25410		* in meters, is not known but phpa, the pressure in hPa (=mB), is
25411		* available, an adequate estimate of hm can be obtained from the
25412		* expression
25413		*
25414		* <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
25415		*
25416		* <p>where tsl is the approximate sea-level air temperature in K
25417		* (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
25418		* 52). Similarly, if the pressure phpa is not known, it can be
25419		* estimated from the height of the observing station, hm, as
25420		* follows:
25421		*
25422		* <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
25423		*
25424		* <p>Note, however, that the refraction is nearly proportional to
25425		* the pressure and that an accurate phpa value is important for
25426		* precise work.
25427		*
25428		* <li> The argument wl specifies the observing wavelength in
25429		* micrometers. The transition from optical to radio is assumed to
25430		* occur at 100 micrometers (about 3000 GHz).
25431		*
25432		* <li> It is advisable to take great care with units, as even unlikely
25433		* values of the input parameters are accepted and processed in
25434		* accordance with the models used.
25435		*
25436		* <li> In cases where the caller wishes to supply his own Earth
25437		* ephemeris, Earth rotation information and refraction constants,
25438		* the function iauApco can be used instead of the present function.
25439		*
25440		* <li> This is one of several functions that inserts into the astrom
25441		* structure star-independent parameters needed for the chain of
25442		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25443		*
25444		* <p>The various functions support different classes of observer and
25445		* portions of the transformation chain:
25446		* <pre>{@literal
25447		* functions observer transformation
25448		*
25449		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
25450		* iauApci iauApci13 terrestrial ICRS <-> CIRS
25451		* iauApco iauApco13 terrestrial ICRS <-> observed
25452		* iauApcs iauApcs13 space ICRS <-> GCRS
25453		* iauAper iauAper13 terrestrial update Earth rotation
25454		* iauApio iauApio13 terrestrial CIRS <-> observed
25455		* }</pre>
25456		* <p>Those with names ending in "13" use contemporary SOFA models to
25457		* compute the various ephemerides. The others accept ephemerides
25458		* supplied by the caller.
25459		*
25460		* <p>The transformation from ICRS to GCRS covers space motion,
25461		* parallax, light deflection, and aberration. From GCRS to CIRS
25462		* comprises frame bias and precession-nutation. From CIRS to
25463		* observed takes account of Earth rotation, polar motion, diurnal
25464		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25465		* transformation), and atmospheric refraction.
25466		*
25467		* <li> The context structure astrom produced by this function is used
25468		* by iauAtioq, iauAtoiq, iauAtciq* and iauAticq*.
25469		*
25470		* </ol>
25471		* Called:
25472		* <ul>
25473		* <li>{@link #jauUtctai} UTC to TAI
25474		* <li>{@link #jauTaitt} TAI to TT
25475		* <li>{@link #jauUtcut1} UTC to UT1
25476		* <li>{@link #jauEpv00} Earth position and velocity
25477		* <li>{@link #jauPnm06a} classical NPB matrix, IAU 2006/2000A
25478		* <li>{@link #jauBpn2xy} extract CIP X,Y coordinates from NPB matrix
25479		* <li>{@link #jauS06} the CIO locator s, given X,Y, IAU 2006
25480		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
25481		* <li>{@link #jauSp00} the TIO locator s', IERS 2000
25482		* <li>{@link #jauRefco} refraction constants for given ambient conditions
25483		* <li>{@link #jauApco} astrometry parameters, ICRS-observed
25484		* <li>{@link #jauEors} equation of the origins, given NPB matrix and s
25485		*
25486		* </ul>
25487		*@version 2013 December 5
25488		*
25489		*@since JSOFA release 20131202
25490		*
25491		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25492		* @throws JSOFAInternalError
25493		* @throws JSOFAIllegalParameter
25494		*/
25495		public static double jauApco13(double utc1, double utc2, double dut1,
25496		double elong, double phi, double hm, double xp, double yp,
25497		double phpa, double tc, double rh, double wl,
25498		Astrom astrom ) throws JSOFAIllegalParameter, JSOFAInternalError
25499		{
25500	10	double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3],
25501		r[][], s, theta, sp;
25502		double eo;
25503
25504
25505		/* UTC to other time scales. */
25506	10	JulianDate tai = jauUtctai(utc1, utc2);
25507	10	JulianDate tt = jauTaitt(tai.djm0, tai.djm1);
25508	10	JulianDate ut1 = jauUtcut1(utc1, utc2, dut1);
25509
25510		/* Earth barycentric & heliocentric position/velocity (au, au/d). */
25511	10	jauEpv00(tt.djm0, tt.djm1, ehpv, ebpv);
25512
25513		/* Form the equinox based BPN matrix, IAU 2006/2000A. */
25514	10	r = jauPnm06a(tt.djm0, tt.djm1);
25515
25516		/* Extract CIP X,Y. */
25517	10	CelestialIntermediatePole cip = jauBpn2xy(r);
25518
25519		/* Obtain CIO locator s. */
25520	10	s = jauS06(tt.djm0, tt.djm1, cip.x, cip.y);
25521
25522		/* Earth rotation angle. */
25523	10	theta = jauEra00(ut1.djm0, ut1.djm1);
25524
25525		/* TIO locator s'. */
25526	10	sp = jauSp00(tt.djm0, tt.djm1);
25527
25528		/* Refraction constants A and B. */
25529	10	RefCos ref = jauRefco(phpa, tc, rh, wl);
25530
25531		/* Compute the star-independent astrometry parameters. */
25532	10	jauApco(tt.djm0, tt.djm1, ebpv, ehpv[0], cip.x, cip.y, s, theta,
25533		elong, phi, hm, xp, yp, sp, ref.a, ref.b, astrom);
25534
25535		/* Equation of the origins. */
25536	10	eo = jauEors(r, s);
25537
25538	10	return eo;
25539
25540		/* Finished. */
25541
25542
25543		}
25544
25545		/**
25546		* For an observer whose geocentric position and velocity are known,
25547		* prepare star-independent astrometry parameters for transformations
25548		* between ICRS and GCRS. The Earth ephemeris is supplied by the
25549		* caller.
25550		*
25551		* The parameters produced by this function are required in the space
25552		* motion, parallax, light deflection and aberration parts of the
25553		* astrometric transformation chain.
25554		*
25555		*<p>This function is derived from the International Astronomical Union's
25556		* SOFA (Standards of Fundamental Astronomy) software collection.
25557		*
25558		*<p>Status: support function.
25559		*
25560		*<!-- Given: -->
25561		* @param date1 double TDB as a 2-part...
25562		* @param date2 double ...Julian Date (Note 1)
25563		* @param pv double[2][3] observer's geocentric pos/vel (m, m/s)
25564		* @param ebpv double[2][3] Earth barycentric PV (au, au/day)
25565		* @param ehp double[3] Earth heliocentric P (au)
25566		*
25567		*<!-- Returned:-->
25568		* @param astrom <b>Returned</b> star-independent astrometry parameters:
25569
25570		*<p>Notes:
25571		* <ol>
25572		*
25573		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25574		* convenient way between the two arguments. For example,
25575		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
25576		* others:
25577		* <pre>
25578		* date1 date2
25579		*
25580		* 2450123.7 0.0 (JD method)
25581		* 2451545.0 -1421.3 (J2000 method)
25582		* 2400000.5 50123.2 (MJD method)
25583		* 2450123.5 0.2 (date & time method)
25584		* </pre>
25585		* <p>The JD method is the most natural and convenient to use in cases
25586		* where the loss of several decimal digits of resolution is
25587		* acceptable. The J2000 method is best matched to the way the
25588		* argument is handled internally and will deliver the optimum
25589		* resolution. The MJD method and the date & time methods are both
25590		* good compromises between resolution and convenience. For most
25591		* applications of this function the choice will not be at all
25592		* critical.
25593		*
25594		* <p>TT can be used instead of TDB without any significant impact on
25595		* accuracy.
25596		*
25597		* <li> All the vectors are with respect to BCRS axes.
25598		*
25599		* <li> Providing separate arguments for (i) the observer's geocentric
25600		* position and velocity and (ii) the Earth ephemeris is done for
25601		* convenience in the geocentric, terrestrial and Earth orbit cases.
25602		* For deep space applications it maybe more convenient to specify
25603		* zero geocentric position and velocity and to supply the
25604		* observer's position and velocity information directly instead of
25605		* with respect to the Earth. However, note the different units:
25606		* m and m/s for the geocentric vectors, au and au/day for the
25607		* heliocentric and barycentric vectors.
25608		*
25609		* <li> In cases where the caller does not wish to provide the Earth
25610		* ephemeris, the function iauApcs13 can be used instead of the
25611		* present function. This computes the Earth ephemeris using the
25612		* SOFA function iauEpv00.
25613		*
25614		* <li> This is one of several functions that inserts into the astrom
25615		* structure star-independent parameters needed for the chain of
25616		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25617		*
25618		* <p>The various functions support different classes of observer and
25619		* portions of the transformation chain:
25620		*
25621		* <pre>{@literal
25622		* functions observer transformation
25623		*
25624		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
25625		* iauApci iauApci13 terrestrial ICRS <-> CIRS
25626		* iauApco iauApco13 terrestrial ICRS <-> observed
25627		* iauApcs iauApcs13 space ICRS <-> GCRS
25628		* iauAper iauAper13 terrestrial update Earth rotation
25629		* iauApio iauApio13 terrestrial CIRS <-> observed
25630		* }</pre>
25631		* <p>Those with names ending in "13" use contemporary SOFA models to
25632		* compute the various ephemerides. The others accept ephemerides
25633		* supplied by the caller.
25634		*
25635		* <p>The transformation from ICRS to GCRS covers space motion,
25636		* parallax, light deflection, and aberration. From GCRS to CIRS
25637		* comprises frame bias and precession-nutation. From CIRS to
25638		* observed takes account of Earth rotation, polar motion, diurnal
25639		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25640		* transformation), and atmospheric refraction.
25641		*
25642		* <li> The context structure astrom produced by this function is used by
25643		* iauAtciq* and iauAticq*.
25644		*
25645		* </ol>
25646		* Called:
25647		* <ul>
25648		* <li>{@link #jauCp} copy p-vector
25649		* <li>{@link #jauPm} modulus of p-vector
25650		* <li>{@link #jauPn} decompose p-vector into modulus and direction
25651		* <li>{@link #jauIr} initialize r-matrix to identity
25652		*
25653		* </ul>
25654		*@version 2013 October 9
25655		*
25656		*@since JSOFA release 20131202
25657		*
25658		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25659		*/
25660		public static void jauApcs(double date1, double date2, double pv[][],
25661		double ebpv[][], double ehp[],
25662		Astrom astrom)
25663		{
25664		/* au/d to m/s */
25665	38	final double AUDMS = DAU/DAYSEC;
25666
25667		/* Light time for 1 AU (day) */
25668	38	final double CR = AULT/DAYSEC;
25669
25670		int i;
25671	38	double dp, dv, pb[] = new double[3], vb[] = new double[3], ph[] = new double[3], v2, w;
25672
25673
25674		/* Time since reference epoch, years (for proper motion calculation). */
25675	38	astrom.pmt = ( (date1 - DJ00) + date2 ) / DJY;
25676
25677		/* Adjust Earth ephemeris to observer. */
25678	152	for (i = 0; i < 3; i++) {
25679	114	dp = pv[0][i] / DAU;
25680	114	dv = pv[1][i] / AUDMS;
25681	114	pb[i] = ebpv[0][i] + dp;
25682	114	vb[i] = ebpv[1][i] + dv;
25683	114	ph[i] = ehp[i] + dp;
25684		}
25685
25686		/* Barycentric position of observer (au). */
25687	38	jauCp(pb, astrom.eb);
25688
25689		/* Heliocentric direction and distance (unit vector and au). */
25690	38	NormalizedVector nv = jauPn(ph);
25691
25692	38	astrom.em = nv.r;
25693	38	astrom.eh = nv.u;
25694
25695		/* Barycentric vel. in units of c, and reciprocal of Lorenz factor. */
25696	38	v2 = 0.0;
25697	152	for (i = 0; i < 3; i++) {
25698	114	w = vb[i] * CR;
25699	114	astrom.v[i] = w;
25700	114	v2 += w*w;
25701		}
25702	38	astrom.bm1 = sqrt(1.0 - v2);
25703
25704		/* Reset the NPB matrix. */
25705	38	jauIr(astrom.bpn);
25706
25707		/* Finished. */
25708
25709
25710	38	}
25711
25712		/**
25713		* For an observer whose geocentric position and velocity are known,
25714		* prepare star-independent astrometry parameters for transformations
25715		* between ICRS and GCRS. The Earth ephemeris is from SOFA models.
25716		*
25717		* The parameters produced by this function are required in the space
25718		* motion, parallax, light deflection and aberration parts of the
25719		* astrometric transformation chain.
25720		*
25721		*<p>This function is derived from the International Astronomical Union's
25722		* SOFA (Standards of Fundamental Astronomy) software collection.
25723		*
25724		*<p>Status: support function.
25725		*
25726		*<!-- Given: -->
25727		* @param date1 double TDB as a 2-part...
25728		* @param date2 double ...Julian Date (Note 1)
25729		* @param pv double[2][3] observer's geocentric pos/vel (Note 3)
25730		*
25731		*<!-- Returned:-->
25732		* @param astrom <b>Returned</b> star-independent astrometry parameters:
25733		*
25734		*<p>Notes:
25735		* <ol>
25736		*
25737		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
25738		* convenient way between the two arguments. For example,
25739		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
25740		* others:
25741		* <pre>
25742		* date1 date2
25743		*
25744		* 2450123.7 0.0 (JD method)
25745		* 2451545.0 -1421.3 (J2000 method)
25746		* 2400000.5 50123.2 (MJD method)
25747		* 2450123.5 0.2 (date & time method)
25748		* </pre>
25749		* <p>The JD method is the most natural and convenient to use in cases
25750		* where the loss of several decimal digits of resolution is
25751		* acceptable. The J2000 method is best matched to the way the
25752		* argument is handled internally and will deliver the optimum
25753		* resolution. The MJD method and the date & time methods are both
25754		* good compromises between resolution and convenience. For most
25755		* applications of this function the choice will not be at all
25756		* critical.
25757		*
25758		* <p>TT can be used instead of TDB without any significant impact on
25759		* accuracy.
25760		*
25761		* <li> All the vectors are with respect to BCRS axes.
25762		*
25763		* <li> The observer's position and velocity pv are geocentric but with
25764		* respect to BCRS axes, and in units of m and m/s. No assumptions
25765		* are made about proximity to the Earth, and the function can be
25766		* used for deep space applications as well as Earth orbit and
25767		* terrestrial.
25768		*
25769		* <li> In cases where the caller wishes to supply his own Earth
25770		* ephemeris, the function iauApcs can be used instead of the present
25771		* function.
25772		*
25773		* <li> This is one of several functions that inserts into the astrom
25774		* structure star-independent parameters needed for the chain of
25775		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25776		*
25777		* <p>The various functions support different classes of observer and
25778		* portions of the transformation chain:
25779		* <pre>{@literal
25780		* functions observer transformation
25781		*
25782		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
25783		* iauApci iauApci13 terrestrial ICRS <-> CIRS
25784		* iauApco iauApco13 terrestrial ICRS <-> observed
25785		* iauApcs iauApcs13 space ICRS <-> GCRS
25786		* iauAper iauAper13 terrestrial update Earth rotation
25787		* iauApio iauApio13 terrestrial CIRS <-> observed
25788		* }</pre>
25789		* <p>Those with names ending in "13" use contemporary SOFA models to
25790		* compute the various ephemerides. The others accept ephemerides
25791		* supplied by the caller.
25792		*
25793		* <p>The transformation from ICRS to GCRS covers space motion,
25794		* parallax, light deflection, and aberration. From GCRS to CIRS
25795		* comprises frame bias and precession-nutation. From CIRS to
25796		* observed takes account of Earth rotation, polar motion, diurnal
25797		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25798		* transformation), and atmospheric refraction.
25799		*
25800		* <li> The context structure astrom produced by this function is used by
25801		* iauAtciq* and iauAticq*.
25802		*
25803		* </ol>
25804		* Called:
25805		* <ul>
25806		* <li>{@link #jauEpv00} Earth position and velocity
25807		* <li>{@link #jauApcs} astrometry parameters, ICRS-GCRS, space observer
25808		*
25809		* </ul>
25810		*@version 2013 October 9
25811		*
25812		*@since JSOFA release 20131202
25813		*
25814		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25815		*/
25816		public static void jauApcs13(double date1, double date2, double pv[][],
25817		Astrom astrom)
25818		{
25819	2	double ehpv[][] = new double[2][3], ebpv[][] = new double[2][3];
25820
25821
25822		/* Earth barycentric & heliocentric position/velocity (au, au/d). */
25823	2	jauEpv00(date1, date2, ehpv, ebpv);
25824
25825		/* Compute the star-independent astrometry parameters. */
25826	2	jauApcs(date1, date2, pv, ebpv, ehpv[0], astrom);
25827
25828		/* Finished. */
25829
25830
25831	2	}
25832
25833		/**
25834		* In the star-independent astrometry parameters, update only the
25835		* Earth rotation angle, supplied by the caller explicitly.
25836		*
25837		*<p>This function is derived from the International Astronomical Union's
25838		* SOFA (Standards of Fundamental Astronomy) software collection.
25839		*
25840		*<p>Status: support function.
25841		*
25842		*<!-- Given: -->
25843		* @param theta double Earth rotation angle (radians, Note 2)
25844		* @param astrom Astrom star-independent astrometry parameters:{@code
25845		* pmt double not used
25846		* eb double[3] not used
25847		* eh double[3] not used
25848		* em double not used
25849		* v double[3] not used
25850		* bm1 double not used
25851		* bpn double[3][3] not used
25852		* along double longitude + s' (radians)
25853		* xpl double not used
25854		* ypl double not used
25855		* sphi double not used
25856		* cphi double not used
25857		* diurab double not used
25858		* eral double not used
25859		* refa double not used
25860		* refb double not used}
25861		*
25862		*<!-- Returned:-->
25863		* astrom <b>Returned</b> star-independent astrometry parameters:
25864		*
25865		*<p>Notes:
25866		* <ol>
25867		*
25868		* <li> This function exists to enable sidereal-tracking applications to
25869		* avoid wasteful recomputation of the bulk of the astrometry
25870		* parameters: only the Earth rotation is updated.
25871		*
25872		* <li> For targets expressed as equinox based positions, such as
25873		* classical geocentric apparent (RA,Dec), the supplied theta can be
25874		* Greenwich apparent sidereal time rather than Earth rotation
25875		* angle.
25876		*
25877		* <li> The function iauAper13 can be used instead of the present
25878		* function, and starts from UT1 rather than ERA itself.
25879		*
25880		* <li> This is one of several functions that inserts into the astrom
25881		* structure star-independent parameters needed for the chain of
25882		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25883		*
25884		* <p>The various functions support different classes of observer and
25885		* portions of the transformation chain:
25886		* <pre>{@literal
25887		* functions observer transformation
25888		*
25889		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
25890		* iauApci iauApci13 terrestrial ICRS <-> CIRS
25891		* iauApco iauApco13 terrestrial ICRS <-> observed
25892		* iauApcs iauApcs13 space ICRS <-> GCRS
25893		* iauAper iauAper13 terrestrial update Earth rotation
25894		* iauApio iauApio13 terrestrial CIRS <-> observed
25895		* }</pre>
25896		* <p>Those with names ending in "13" use contemporary SOFA models to
25897		* compute the various ephemerides. The others accept ephemerides
25898		* supplied by the caller.
25899		*
25900		* <p>The transformation from ICRS to GCRS covers space motion,
25901		* parallax, light deflection, and aberration. From GCRS to CIRS
25902		* comprises frame bias and precession-nutation. From CIRS to
25903		* observed takes account of Earth rotation, polar motion, diurnal
25904		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
25905		* transformation), and atmospheric refraction.
25906		*
25907		* </ol>
25908		*@version 2013 September 25
25909		*
25910		*@since JSOFA release 20131202
25911		*
25912		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
25913		*/
25914		public static void jauAper(double theta, Astrom astrom)
25915		{
25916	32	astrom.eral = theta + astrom.along;
25917
25918		/* Finished. */
25919
25920
25921	32	}
25922
25923		/**
25924		* In the star-independent astrometry parameters, update only the
25925		* Earth rotation angle. The caller provides UT1, (n.b. not UTC).
25926		*
25927		*<p>This function is derived from the International Astronomical Union's
25928		* SOFA (Standards of Fundamental Astronomy) software collection.
25929		*
25930		*<p>Status: support function.
25931		*
25932		*<!-- Given: -->
25933		* @param ut11 double UT1 as a 2-part...
25934		* @param ut12 double ...Julian Date (Note 1)
25935		* @param astrom star-independent astrometry parameters:
25936		* pmt double not used
25937		* eb double[3] not used
25938		* eh double[3] not used
25939		* em double not used
25940		* v double[3] not used
25941		* bm1 double not used
25942		* bpn double[3][3] not used
25943		* along double longitude + s' (radians)
25944		* xpl double not used
25945		* ypl double not used
25946		* sphi double not used
25947		* cphi double not used
25948		* diurab double not used
25949		* eral double not used
25950		* refa double not used
25951		* refb double not used
25952		*
25953		*<!-- Returned:-->
25954		* @param astrom <b>Returned</b> star-independent astrometry parameters:
25955		*
25956		*<p>Notes:
25957		* <ol>
25958		*
25959		* <li> The UT1 date (n.b. not UTC) ut11+ut12 is a Julian Date,
25960		* apportioned in any convenient way between the arguments ut11 and
25961		* ut12. For example, JD(UT1)=2450123.7 could be expressed in any
25962		* of these ways, among others:
25963		*
25964		* <p>ut11 ut12
25965		*
25966		* 2450123.7 0.0 (JD method)
25967		* 2451545.0 -1421.3 (J2000 method)
25968		* 2400000.5 50123.2 (MJD method)
25969		* 2450123.5 0.2 (date & time method)
25970		*
25971		* <p>The JD method is the most natural and convenient to use in cases
25972		* where the loss of several decimal digits of resolution is
25973		* acceptable. The J2000 and MJD methods are good compromises
25974		* between resolution and convenience. The date & time method is
25975		* best matched to the algorithm used: maximum precision is
25976		* delivered when the ut11 argument is for 0hrs UT1 on the day in
25977		* question and the ut12 argument lies in the range 0 to 1, or vice
25978		* versa.
25979		*
25980		* <li> If the caller wishes to provide the Earth rotation angle itself,
25981		* the function iauAper can be used instead. One use of this
25982		* technique is to substitute Greenwich apparent sidereal time and
25983		* thereby to support equinox based transformations directly.
25984		*
25985		* <li> This is one of several functions that inserts into the astrom
25986		* structure star-independent parameters needed for the chain of
25987		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
25988		*
25989		* <p>The various functions support different classes of observer and
25990		* portions of the transformation chain:
25991		* <pre>{@literal
25992		* functions observer transformation
25993		*
25994		* <p>iauApcg iauApcg13 geocentric ICRS <-> GCRS
25995		* iauApci iauApci13 terrestrial ICRS <-> CIRS
25996		* iauApco iauApco13 terrestrial ICRS <-> observed
25997		* iauApcs iauApcs13 space ICRS <-> GCRS
25998		* iauAper iauAper13 terrestrial update Earth rotation
25999		* iauApio iauApio13 terrestrial CIRS <-> observed
26000		* }</pre>
26001		* <p>Those with names ending in "13" use contemporary SOFA models to
26002		* compute the various ephemerides. The others accept ephemerides
26003		* supplied by the caller.
26004		*
26005		* <p>The transformation from ICRS to GCRS covers space motion,
26006		* parallax, light deflection, and aberration. From GCRS to CIRS
26007		* comprises frame bias and precession-nutation. From CIRS to
26008		* observed takes account of Earth rotation, polar motion, diurnal
26009		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
26010		* transformation), and atmospheric refraction.
26011		*
26012		* </ol>
26013		* Called:
26014		* <ul>
26015		* <li>{@link #jauAper} astrometry parameters: update ERA
26016		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
26017		*
26018		* </ul>
26019		*@version 2013 September 25
26020		*
26021		*@since JSOFA release 20131202
26022		*
26023		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26024		*/
26025		public static void jauAper13(double ut11, double ut12, Astrom astrom)
26026		{
26027	2	jauAper(jauEra00(ut11,ut12), astrom);
26028
26029		/* Finished. */
26030
26031
26032	2	}
26033
26034		/**
26035		* For a terrestrial observer, prepare star-independent astrometry
26036		* parameters for transformations between CIRS and observed
26037		* coordinates. The caller supplies the Earth orientation information
26038		* and the refraction constants as well as the site coordinates.
26039		*
26040		*<p>This function is derived from the International Astronomical Union's
26041		* SOFA (Standards of Fundamental Astronomy) software collection.
26042		*
26043		*<p>Status: support function.
26044		*
26045		*<!-- Given: -->
26046		* @param sp double the TIO locator s' (radians, Note 1)
26047		* @param theta double Earth rotation angle (radians)
26048		* @param elong double longitude (radians, east +ve, Note 2)
26049		* @param phi double geodetic latitude (radians, Note 2)
26050		* @param hm double height above ellipsoid (m, geodetic Note 2)
26051		* @param xp double polar motion coordinates (radians, Note 3)
26052		* @param yp double polar motion coordinates (radians, Note 3)
26053		* @param refa double refraction constant A (radians, Note 4)
26054		* @param refb double refraction constant B (radians, Note 4)
26055		*
26056		*<!-- Returned:-->
26057		* @param astrom {@link Astrom} <b>Returned</b> star-independent astrometry parameters:
26058		*
26059		*<p>Notes:
26060		* <ol>
26061		*
26062		* <li> sp, the TIO locator s', is a tiny quantity needed only by the
26063		* most precise applications. It can either be set to zero or
26064		* predicted using the SOFA function iauSp00.
26065		*
26066		* <li> The geographical coordinates are with respect to the WGS84
26067		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
26068		* longitude required by the present function is east-positive
26069		* (i.e. right-handed), in accordance with geographical convention.
26070		*
26071		* <li> The polar motion xp,yp can be obtained from IERS bulletins. The
26072		* values are the coordinates (in radians) of the Celestial
26073		* Intermediate Pole with respect to the International Terrestrial
26074		* Reference System (see IERS Conventions 2003), measured along the
26075		* meridians 0 and 90 deg west respectively. For many applications,
26076		* xp and yp can be set to zero.
26077		*
26078		* <p>Internally, the polar motion is stored in a form rotated onto the
26079		* local meridian.
26080		*
26081		* <li> The refraction constants refa and refb are for use in a
26082		* dZ = Atan(Z)+Btan^3(Z) model, where Z is the observed
26083		* (i.e. refracted) zenith distance and dZ is the amount of
26084		* refraction.
26085		*
26086		* <li> It is advisable to take great care with units, as even unlikely
26087		* values of the input parameters are accepted and processed in
26088		* accordance with the models used.
26089		*
26090		* <li> In cases where the caller does not wish to provide the Earth
26091		* rotation information and refraction constants, the function
26092		* iauApio13 can be used instead of the present function. This
26093		* starts from UTC and weather readings etc. and computes suitable
26094		* values using other SOFA functions.
26095		*
26096		* <li> This is one of several functions that inserts into the astrom
26097		* structure star-independent parameters needed for the chain of
26098		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
26099		*
26100		* <p>The various functions support different classes of observer and
26101		* portions of the transformation chain:
26102		*<pre>{@literal
26103		* functions observer transformation
26104		*
26105		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
26106		* iauApci iauApci13 terrestrial ICRS <-> CIRS
26107		* iauApco iauApco13 terrestrial ICRS <-> observed
26108		* iauApcs iauApcs13 space ICRS <-> GCRS
26109		* iauAper iauAper13 terrestrial update Earth rotation
26110		* iauApio iauApio13 terrestrial CIRS <-> observed
26111		*}</pre>
26112		* <p>Those with names ending in "13" use contemporary SOFA models to
26113		* compute the various ephemerides. The others accept ephemerides
26114		* supplied by the caller.
26115		*
26116		* <p>The transformation from ICRS to GCRS covers space motion,
26117		* parallax, light deflection, and aberration. From GCRS to CIRS
26118		* comprises frame bias and precession-nutation. From CIRS to
26119		* observed takes account of Earth rotation, polar motion, diurnal
26120		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
26121		* transformation), and atmospheric refraction.
26122		*
26123		* <li> The context structure astrom produced by this function is used by
26124		* iauAtioq and iauAtoiq.
26125		*
26126		* </ol>
26127		* Called:
26128		* <ul>
26129		* <li>{@link #jauPvtob} position/velocity of terrestrial station
26130		* <li>{@link #jauAper} astrometry parameters: update ERA
26131		*
26132		* </ul>
26133		*@version 2013 October 9
26134		*
26135		*@since JSOFA release 20131202
26136		*
26137		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26138		* @throws JSOFAInternalError
26139		* @throws JSOFAIllegalParameter
26140		*/
26141		public static void jauApio(double sp, double theta,
26142		double elong, double phi, double hm, double xp, double yp,
26143		double refa, double refb,
26144		Astrom astrom) throws JSOFAIllegalParameter, JSOFAInternalError
26145		{
26146		double sl, cl, pv[][];
26147
26148
26149		/* Longitude with adjustment for TIO locator s'. */
26150	16	astrom.along = elong + sp;
26151
26152		/* Polar motion, rotated onto the local meridian. */
26153	16	sl = sin(astrom.along);
26154	16	cl = cos(astrom.along);
26155	16	astrom.xpl = xpcl - ypsl;
26156	16	astrom.ypl = xpsl + ypcl;
26157
26158		/* Functions of latitude. */
26159	16	astrom.sphi = sin(phi);
26160	16	astrom.cphi = cos(phi);
26161
26162		/* Observer's geocentric position and velocity (m, m/s, CIRS). */
26163	16	pv = jauPvtob(elong, phi, hm, xp, yp, sp, theta);
26164
26165		/* Magnitude of diurnal aberration vector. */
26166	16	astrom.diurab = sqrt(pv[1][0]pv[1][0]+pv[1][1]pv[1][1]) / CMPS;
26167
26168		/* Refraction constants. */
26169	16	astrom.refa = refa;
26170	16	astrom.refb = refb;
26171
26172		/* Local Earth rotation angle. */
26173	16	jauAper(theta, astrom);
26174
26175		/* Finished. */
26176
26177
26178	16	}
26179
26180		/**
26181		* For a terrestrial observer, prepare star-independent astrometry
26182		* parameters for transformations between CIRS and observed
26183		* coordinates. The caller supplies UTC, site coordinates, ambient air
26184		* conditions and observing wavelength.
26185		*
26186		*<p>This function is derived from the International Astronomical Union's
26187		* SOFA (Standards of Fundamental Astronomy) software collection.
26188		*
26189		*<p>Status: support function.
26190		*
26191		*<!-- Given: -->
26192		* @param utc1 double UTC as a 2-part...
26193		* @param utc2 double ...quasi Julian Date (Notes 1,2)
26194		* @param dut1 double UT1-UTC (seconds)
26195		* @param elong double longitude (radians, east +ve, Note 3)
26196		* @param phi double geodetic latitude (radians, Note 3)
26197		* @param hm double height above ellipsoid (m, geodetic Notes 4,6)
26198		* @param xp double polar motion coordinates (radians, Note 5)
26199		* @param yp double polar motion coordinates (radians, Note 5)
26200		* @param phpa double pressure at the observer (hPa = mB, Note 6)
26201		* @param tc double ambient temperature at the observer (deg C)
26202		* @param rh double relative humidity at the observer (range 0-1)
26203		* @param wl double wavelength (micrometers, Note 7)
26204		*
26205		*<!-- Returned:-->
26206		* @param astrom <b>Returned</b> star-independent astrometry parameters:
26207		* @throws JSOFAInternalError
26208		* @throws JSOFAIllegalParameter
26209		*
26210		* int status: <b>Returned</b> +1 = dubious year (Note 2)
26211		* 0 = <b>Returned</b> OK
26212		* -1 = <b>Returned</b> unacceptable date
26213		*
26214		*<p>Notes:
26215		* <ol>
26216		*
26217		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
26218		* convenient way between the two arguments, for example where utc1
26219		* is the Julian Day Number and utc2 is the fraction of a day.
26220		*
26221		* <p>However, JD cannot unambiguously represent UTC during a leap
26222		* second unless special measures are taken. The convention in the
26223		* present function is that the JD day represents UTC days whether
26224		* the length is 86399, 86400 or 86401 SI seconds.
26225		*
26226		* <p>Applications should use the function iauDtf2d to convert from
26227		* calendar date and time of day into 2-part quasi Julian Date, as
26228		* it implements the leap-second-ambiguity convention just
26229		* described.
26230		*
26231		* <li> The warning status "dubious year" flags UTCs that predate the
26232		* introduction of the time scale or that are too far in the future
26233		* to be trusted. See iauDat for further details.
26234		*
26235		* <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
26236		* one second at the end of each positive UTC leap second,
26237		* introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
26238		* practice is under review, and in the future UT1-UTC may grow
26239		* essentially without limit.
26240		*
26241		* <li> The geographical coordinates are with respect to the WGS84
26242		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
26243		* longitude required by the present function is east-positive
26244		* (i.e. right-handed), in accordance with geographical convention.
26245		*
26246		* <li> The polar motion xp,yp can be obtained from IERS bulletins. The
26247		* values are the coordinates (in radians) of the Celestial
26248		* Intermediate Pole with respect to the International Terrestrial
26249		* Reference System (see IERS Conventions 2003), measured along the
26250		* meridians 0 and 90 deg west respectively. For many applications,
26251		* xp and yp can be set to zero.
26252		*
26253		* <p>Internally, the polar motion is stored in a form rotated onto
26254		* the local meridian.
26255		*
26256		* <li> If hm, the height above the ellipsoid of the observing station
26257		* in meters, is not known but phpa, the pressure in hPa (=mB), is
26258		* available, an adequate estimate of hm can be obtained from the
26259		* expression
26260		*
26261		* <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
26262		*
26263		* <p>where tsl is the approximate sea-level air temperature in K
26264		* (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
26265		* 52). Similarly, if the pressure phpa is not known, it can be
26266		* estimated from the height of the observing station, hm, as
26267		* follows:
26268		*
26269		* <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
26270		*
26271		* <p>Note, however, that the refraction is nearly proportional to the
26272		* pressure and that an accurate phpa value is important for
26273		* precise work.
26274		*
26275		* <li> The argument wl specifies the observing wavelength in
26276		* micrometers. The transition from optical to radio is assumed to
26277		* occur at 100 micrometers (about 3000 GHz).
26278		*
26279		* <li> It is advisable to take great care with units, as even unlikely
26280		* values of the input parameters are accepted and processed in
26281		* accordance with the models used.
26282		*
26283		* <li> In cases where the caller wishes to supply his own Earth
26284		* rotation information and refraction constants, the function
26285		* iauApc can be used instead of the present function.
26286		*
26287		* <li> This is one of several functions that inserts into the astrom
26288		* structure star-independent parameters needed for the chain of
26289		* astrometric transformations {@literal ICRS <-> GCRS <-> CIRS <-> observed.}
26290		*
26291		* <p>The various functions support different classes of observer and
26292		* portions of the transformation chain:
26293		* <pre>{@literal
26294		* functions observer transformation
26295		*
26296		* iauApcg iauApcg13 geocentric ICRS <-> GCRS
26297		* iauApci iauApci13 terrestrial ICRS <-> CIRS
26298		* iauApco iauApco13 terrestrial ICRS <-> observed
26299		* iauApcs iauApcs13 space ICRS <-> GCRS
26300		* iauAper iauAper13 terrestrial update Earth rotation
26301		* iauApio iauApio13 terrestrial CIRS <-> observed
26302		* }</pre>
26303		* <p>Those with names ending in "13" use contemporary SOFA models to
26304		* compute the various ephemerides. The others accept ephemerides
26305		* supplied by the caller.
26306		*
26307		* <p>The transformation from ICRS to GCRS covers space motion,
26308		* parallax, light deflection, and aberration. From GCRS to CIRS
26309		* comprises frame bias and precession-nutation. From CIRS to
26310		* observed takes account of Earth rotation, polar motion, diurnal
26311		* aberration and parallax (unless subsumed into the {@literal ICRS <-> GCRS}
26312		* transformation), and atmospheric refraction.
26313		*
26314		* <li> The context structure astrom produced by this function is used
26315		* by iauAtioq and iauAtoiq.
26316		*
26317		* </ol>
26318		* Called:
26319		* <ul>
26320		* <li>{@link #jauUtctai} UTC to TAI
26321		* <li>{@link #jauTaitt} TAI to TT
26322		* <li>{@link #jauUtcut1} UTC to UT1
26323		* <li>{@link #jauSp00} the TIO locator s', IERS 2000
26324		* <li>{@link #jauEra00} Earth rotation angle, IAU 2000
26325		* <li>{@link #jauRefco} refraction constants for given ambient conditions
26326		* <li>{@link #jauApio} astrometry parameters, CIRS-observed
26327		*
26328		* </ul>
26329		*@version 2013 October 9
26330		*
26331		*@since JSOFA release 20131202
26332		*
26333		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26334		* @throws JSOFAInternalError
26335		* @throws JSOFAIllegalParameter
26336		*/
26337		public static void jauApio13(double utc1, double utc2, double dut1,
26338		double elong, double phi, double hm, double xp, double yp,
26339		double phpa, double tc, double rh, double wl,
26340		Astrom astrom) throws JSOFAIllegalParameter, JSOFAInternalError
26341		{
26342		double sp, theta;
26343
26344
26345		/* UTC to other time scales. */
26346	14	JulianDate tai = jauUtctai(utc1, utc2);
26347	14	JulianDate tt = jauTaitt(tai.djm0, tai.djm1);
26348	14	JulianDate ut1 = jauUtcut1(utc1, utc2, dut1);
26349
26350		/* TIO locator s'. */
26351	14	sp = jauSp00(tt.djm0, tt.djm1);
26352
26353		/* Earth rotation angle. */
26354	14	theta = jauEra00(ut1.djm0, ut1.djm1);
26355
26356		/* Refraction constants A and B. */
26357	14	RefCos refco = jauRefco(phpa, tc, rh, wl);
26358
26359		/* CIRS <-> observed astrometry parameters. */
26360	14	jauApio(sp, theta, elong, phi, hm, xp, yp, refco.a, refco.b, astrom);
26361
26362
26363		/* Finished. */
26364
26365
26366	14	}
26367
26368		/**
26369		* Transform ICRS star data, epoch J2000.0, to CIRS.
26370		*
26371		*<p>This function is derived from the International Astronomical Union's
26372		* SOFA (Standards of Fundamental Astronomy) software collection.
26373		*
26374		*<p>Status: support function.
26375		*
26376		*<!-- Given: -->
26377		* @param rc double ICRS right ascension at J2000.0 (radians, Note 1)
26378		* @param dc double ICRS declination at J2000.0 (radians, Note 1)
26379		* @param pr double RA proper motion (radians/year; Note 2)
26380		* @param pd double Dec proper motion (radians/year)
26381		* @param px double parallax (arcsec)
26382		* @param rv double radial velocity (km/s, +ve if receding)
26383		* @param date1 double TDB as a 2-part...
26384		* @param date2 double ...Julian Date (Note 3)
26385		*
26386		*<!-- Returned:-->
26387		* @return double* <b>Returned</b> CIRS geocentric RA,Dec (radians)
26388		* eo double* <b>Returned</b> equation of the origins (ERA-GST, Note 5)
26389		*
26390		*<p>Notes:
26391		* <ol>
26392		*
26393		* <li> Star data for an epoch other than J2000.0 (for example from the
26394		* Hipparcos catalog, which has an epoch of J1991.25) will require a
26395		* preliminary call to iauPmsafe before use.
26396		*
26397		* <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26398		*
26399		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
26400		* convenient way between the two arguments. For example,
26401		* JD(TDB)=2450123.8g could be expressed in any of these ways, among
26402		* others:
26403		*
26404		* date1 date2
26405		*
26406		* 2450123.8g 0.0 (JD method)
26407		* 2451545.0 -1421.3 (J2000 method)
26408		* 2400000.5 50123.2 (MJD method)
26409		* 2450123.5 0.2 (date & time method)
26410		*
26411		* <p>The JD method is the most natural and convenient to use in cases
26412		* where the loss of several decimal digits of resolution is
26413		* acceptable. The J2000 method is best matched to the way the
26414		* argument is handled internally and will deliver the optimum
26415		* resolution. The MJD method and the date & time methods are both
26416		* good compromises between resolution and convenience. For most
26417		* applications of this function the choice will not be at all
26418		* critical.
26419		*
26420		* <p>TT can be used instead of TDB without any significant impact on
26421		* accuracy.
26422		*
26423		* <li> The available accuracy is better than 1 milliarcsecond, limited
26424		* mainly by the precession-nutation model that is used, namely
26425		* IAU 2000A/2006. Very close to solar system bodies, additional
26426		* errors of up to several milliarcseconds can occur because of
26427		* unmodeled light deflection; however, the Sun's contribution is
26428		* taken into account, to first order. The accuracy limitations of
26429		* the SOFA function iauEpv00 (used to compute Earth position and
26430		* velocity) can contribute aberration errors of up to
26431		* 5 microarcseconds. Light deflection at the Sun's limb is
26432		* uncertain at the 0.4 mas level.
26433		*
26434		* <li> Should the transformation to (equinox based) apparent place be
26435		* required rather than (CIO based) intermediate place, subtract the
26436		* equation of the origins from the returned right ascension:
26437		* RA = RI - EO. (The iauAnp function can then be applied, as
26438		* required, to keep the result in the conventional 0-2pi range.)
26439		*
26440		* </ol>
26441		* Called:
26442		* <ul>
26443		* <li>{@link #jauApci13} astrometry parameters, ICRS-CIRS, 2013
26444		* <li>{@link #jauAtciq} quick ICRS to CIRS
26445		*
26446		* </ul>
26447		*@version 2013 October 9
26448		*
26449		*@since JSOFA release 20131202
26450		*
26451		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26452		*/
26453		public static SphericalCoordinateEO jauAtci13(double rc, double dc,
26454		double pr, double pd, double px, double rv,
26455		double date1, double date2)
26456		{
26457		/* Star-independent astrometry parameters */
26458	2	Astrom astrom = new Astrom();
26459
26460
26461		/* The transformation parameters. */
26462	2	double eo = jauApci13(date1, date2, astrom);
26463
26464		/* ICRS (epoch J2000.0) to CIRS. */
26465	2	SphericalCoordinate co = jauAtciq(rc, dc, pr, pd, px, rv, astrom);
26466
26467	2	return new SphericalCoordinateEO(co, eo);
26468		/* Finished. */
26469
26470
26471		}
26472
26473		/**
26474		* Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed
26475		* star-independent astrometry parameters.
26476		*
26477		* Use of this function is appropriate when efficiency is important and
26478		* where many star positions are to be transformed for one date. The
26479		* star-independent parameters can be obtained by calling one of the
26480		* functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
26481		*
26482		* If the parallax and proper motions are zero the iauAtciqz function
26483		* can be used instead.
26484		*
26485		*<p>This function is derived from the International Astronomical Union's
26486		* SOFA (Standards of Fundamental Astronomy) software collection.
26487		*
26488		*<p>Status: support function.
26489		*
26490		*<!-- Given: -->
26491		* @param rc double ICRS RA,Dec at J2000.0 (radians)
26492		* @param dc double ICRS RA,Dec at J2000.0 (radians)
26493		* @param pr double RA proper motion (radians/year; Note 3)
26494		* @param pd double Dec proper motion (radians/year)
26495		* @param px double parallax (arcsec)
26496		* @param rv double radial velocity (km/s, +ve if receding)
26497		* @param astrom star-independent astrometry parameters:
26498		*
26499		*<!-- Returned:-->
26500		* @return double <b>Returned</b> CIRS RA,Dec (radians)
26501		*
26502		*<p>Notes:
26503		* <ol>
26504		*
26505		* <li> All the vectors are with respect to BCRS axes.
26506		*
26507		* <li> Star data for an epoch other than J2000.0 (for example from the
26508		* Hipparcos catalog, which has an epoch of J1991.25) will require a
26509		* preliminary call to iauPmsafe before use.
26510		*
26511		* <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26512		*
26513		* </ol>
26514		* Called:
26515		* <ul>
26516		* <li>{@link #jauPmpx} proper motion and parallax
26517		* <li>{@link #jauLdsun} light deflection by the Sun
26518		* <li>{@link #jauAb} stellar aberration
26519		* <li>{@link #jauRxp} product of r-matrix and pv-vector
26520		* <li>{@link #jauC2s} p-vector to spherical
26521		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
26522		*
26523		* </ul>
26524		*@version 2013 October 9
26525		*
26526		*@since JSOFA release 20131202
26527		*
26528		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26529		*/
26530		public static SphericalCoordinate jauAtciq(double rc, double dc,
26531		double pr, double pd, double px, double rv,
26532		Astrom astrom)
26533		{
26534		double pco[], pnat[], ppr[], pi[];
26535
26536
26537		/* Proper motion and parallax, giving BCRS coordinate direction. */
26538	6	pco = jauPmpx(rc, dc, pr, pd, px, rv, astrom.pmt, astrom.eb);
26539
26540		/* Light deflection by the Sun, giving BCRS natural direction. */
26541	6	pnat = jauLdsun(pco, astrom.eh, astrom.em);
26542
26543		/* Aberration, giving GCRS proper direction. */
26544	6	ppr = jauAb(pnat, astrom.v, astrom.em, astrom.bm1);
26545
26546		/* Bias-precession-nutation, giving CIRS proper direction. */
26547	6	pi = jauRxp(astrom.bpn, ppr);
26548
26549		/* CIRS RA,Dec. */
26550	6	SphericalCoordinate co = jauC2s(pi);
26551	6	co.alpha = jauAnp(co.alpha);
26552
26553	6	return co;
26554		/* Finished. */
26555
26556
26557		}
26558
26559		/**
26560		* Quick ICRS, epoch J2000.0, to CIRS transformation, given precomputed
26561		* star-independent astrometry parameters plus a list of light-
26562		* deflecting bodies.
26563		*
26564		* Use of this function is appropriate when efficiency is important and
26565		* where many star positions are to be transformed for one date. The
26566		* star-independent parameters can be obtained by calling one of the
26567		* functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
26568		*
26569		*
26570		* If the only light-deflecting body to be taken into account is the
26571		* Sun, the iauAtciq function can be used instead. If in addition the
26572		* parallax and proper motions are zero, the iauAtciqz function can be
26573		* used.
26574		*
26575		*<p>This function is derived from the International Astronomical Union's
26576		* SOFA (Standards of Fundamental Astronomy) software collection.
26577		*
26578		*<p>Status: support function.
26579		*
26580		*<!-- Given: -->
26581		* @param rc double ICRS RA,Dec at J2000.0 (radians)
26582		* @param dc double ICRS RA,Dec at J2000.0 (radians)
26583		* @param pr double RA proper motion (radians/year; Note 3)
26584		* @param pd double Dec proper motion (radians/year)
26585		* @param px double parallax (arcsec)
26586		* @param rv double radial velocity (km/s, +ve if receding)
26587		* @param astrom star-independent astrometry parameters:
26588		* @param n int number of bodies (Note 3)
26589		* @param b jauLDBODY[n] data for each of the n bodies (Notes 3,4):
26590		*
26591		*<!-- Returned:-->
26592		* @return ri,di double <b>Returned</b> CIRS RA,Dec (radians)
26593		*
26594		*<p>Notes:
26595		* <ol>
26596		*
26597		* <li> Star data for an epoch other than J2000.0 (for example from the
26598		* Hipparcos catalog, which has an epoch of J1991.25) will require a
26599		* preliminary call to iauPmsafe before use.
26600		*
26601		* <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26602		*
26603		* <li> The struct b contains n entries, one for each body to be
26604		* considered. If n = 0, no gravitational light deflection will be
26605		* applied, not even for the Sun.
26606		*
26607		* <li> The struct b should include an entry for the Sun as well as for
26608		* any planet or other body to be taken into account. The entries
26609		* should be in the order in which the light passes the body.
26610		*
26611		* <li> In the entry in the b struct for body i, the mass parameter
26612		* b[i].bm can, as required, be adjusted in order to allow for such
26613		* effects as quadrupole field.
26614		*
26615		* <li> The deflection limiter parameter b[i].dl is phi^2/2, where phi is
26616		* the angular separation (in radians) between star and body at
26617		* which limiting is applied. As phi shrinks below the chosen
26618		* threshold, the deflection is artificially reduced, reaching zero
26619		* for phi = 0. Example values suitable for a terrestrial
26620		* observer, together with masses, are as follows:
26621		* <pre>
26622		* body i b[i].bm b[i].dl
26623		*
26624		* Sun 1.0 6e-6
26625		* Jupiter 0.00095435 3e-9
26626		* Saturn 0.00028574 3e-10
26627		* </pre>
26628		* <li> For efficiency, validation of the contents of the b array is
26629		* omitted. The supplied masses must be greater than zero, the
26630		* position and velocity vectors must be right, and the deflection
26631		* limiter greater than zero.
26632		*
26633		* </ol>
26634		* Called:
26635		* <ul>
26636		* <li>{@link #jauPmpx} proper motion and parallax
26637		* <li>{@link #jauLdn} light deflection by n bodies
26638		* <li>{@link #jauAb} stellar aberration
26639		* <li>{@link #jauRxp} product of r-matrix and pv-vector
26640		* <li>{@link #jauC2s} p-vector to spherical
26641		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
26642		*
26643		* </ul>
26644		*@version 2013 October 9
26645		*
26646		*@since JSOFA release 20131202
26647		*
26648		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26649		*/
26650		public static SphericalCoordinate jauAtciqn(double rc, double dc, double pr, double pd,
26651		double px, double rv, Astrom astrom,
26652		int n, Ldbody b[])
26653		{
26654	2	double pco[], pnat[], ppr[] = new double[3], pi[] = new double[3];
26655
26656
26657		/* Proper motion and parallax, giving BCRS coordinate direction. */
26658	2	pco = jauPmpx(rc, dc, pr, pd, px, rv, astrom.pmt, astrom.eb);
26659
26660		/* Light deflection, giving BCRS natural direction. */
26661	2	pnat = jauLdn(n, b, astrom.eb, pco);
26662
26663		/* Aberration, giving GCRS proper direction. */
26664	2	ppr = jauAb(pnat, astrom.v, astrom.em, astrom.bm1);
26665
26666		/* Bias-precession-nutation, giving CIRS proper direction. */
26667	2	pi = jauRxp(astrom.bpn, ppr);
26668
26669		/* CIRS RA,Dec. */
26670	2	SphericalCoordinate co = jauC2s(pi);
26671	2	co.alpha = jauAnp(co.alpha);
26672
26673	2	return co;
26674		/* Finished. */
26675
26676
26677		}
26678
26679		/**
26680		* Quick ICRS to CIRS transformation, given precomputed star-
26681		* independent astrometry parameters, and assuming zero parallax and
26682		* proper motion.
26683		*
26684		* Use of this function is appropriate when efficiency is important and
26685		* where many star positions are to be transformed for one date. The
26686		* star-independent parameters can be obtained by calling one of the
26687		* functions iauApci[13], iauApcg[13], iauApco[13] or iauApcs[13].
26688		*
26689		* The corresponding function for the case of non-zero parallax and
26690		* proper motion is iauAtciq.
26691		*
26692		*<p>This function is derived from the International Astronomical Union's
26693		* SOFA (Standards of Fundamental Astronomy) software collection.
26694		*
26695		*<p>Status: support function.
26696		*
26697		*<!-- Given: -->
26698		* @param rc double ICRS astrometric RA,Dec (radians)
26699		* @param dc double ICRS astrometric RA,Dec (radians)
26700		* @param astrom star-independent astrometry parameters:
26701		*
26702		*<!-- Returned:-->
26703		* @return ri,di double <b>Returned</b> CIRS RA,Dec (radians)
26704		*
26705		* Note:
26706		*
26707		* @return All the <b>Returned</b> vectors are with respect to BCRS axes.
26708		*
26709		*<p>References:
26710		* <ul>
26711		*
26712		* <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
26713		* the Astronomical Almanac, 3rd ed., University Science Books
26714		* (2013).
26715		*
26716		* <li> Klioner, Sergei A., "A practical relativistic model for micro-
26717		* arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
26718		*
26719		* </ul>
26720		* Called:
26721		* <ul>
26722		* <li>{@link #jauS2c} spherical coordinates to unit vector
26723		* <li>{@link #jauLdsun} light deflection due to Sun
26724		* <li>{@link #jauAb} stellar aberration
26725		* <li>{@link #jauRxp} product of r-matrix and p-vector
26726		* <li>{@link #jauC2s} p-vector to spherical
26727		* <li>{@link #jauAnp} normalize angle into range +/- pi
26728		*
26729		* </ul>
26730		*@version 2013 October 9
26731		*
26732		*@since JSOFA release 20131202
26733		*
26734		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26735		*/
26736		public static SphericalCoordinate jauAtciqz(double rc, double dc, Astrom astrom)
26737		{
26738	2	double pco[], pnat[], ppr[] = new double[3], pi[];
26739
26740
26741		/* BCRS coordinate direction (unit vector). */
26742	2	pco = jauS2c(rc, dc);
26743
26744		/* Light deflection by the Sun, giving BCRS natural direction. */
26745	2	pnat = jauLdsun(pco, astrom.eh, astrom.em);
26746
26747		/* Aberration, giving GCRS proper direction. */
26748	2	ppr = jauAb(pnat, astrom.v, astrom.em, astrom.bm1);
26749
26750		/* Bias-precession-nutation, giving CIRS proper direction. */
26751	2	pi = jauRxp(astrom.bpn, ppr);
26752
26753		/* CIRS RA,Dec. */
26754	2	SphericalCoordinate co = jauC2s(pi);
26755	2	co.alpha = jauAnp(co.alpha);
26756
26757	2	return co;
26758		/* Finished. */
26759
26760
26761		}
26762
26763		/**
26764		* ICRS RA,Dec to observed place. The caller supplies UTC, site
26765		* coordinates, ambient air conditions and observing wavelength.
26766		*
26767		* SOFA models are used for the Earth ephemeris, bias-precession-
26768		* nutation, Earth orientation and refraction.
26769		*
26770		*<p>This function is derived from the International Astronomical Union's
26771		* SOFA (Standards of Fundamental Astronomy) software collection.
26772		*
26773		*<p>Status: support function.
26774		*
26775		*<!-- Given: -->
26776		* @param rc double ICRS right ascension at J2000.0 (radians, Note 1)
26777		* @param dc double ICRS right ascension at J2000.0 (radians, Note 1)
26778		* @param pr double RA proper motion (radians/year; Note 2)
26779		* @param pd double Dec proper motion (radians/year)
26780		* @param px double parallax (arcsec)
26781		* @param rv double radial velocity (km/s, +ve if receding)
26782		* @param utc1 double UTC as a 2-part...
26783		* @param utc2 double ...quasi Julian Date (Notes 3-4)
26784		* @param dut1 double UT1-UTC (seconds, Note 5)
26785		* @param elong double longitude (radians, east +ve, Note 6)
26786		* @param phi double latitude (geodetic, radians, Note 6)
26787		* @param hm double height above ellipsoid (m, geodetic, Notes 6,8)
26788		* @param xp double polar motion coordinates (radians, Note 7)
26789		* @param yp double polar motion coordinates (radians, Note 7)
26790		* @param phpa double pressure at the observer (hPa = mB, Note 8)
26791		* @param tc double ambient temperature at the observer (deg C)
26792		* @param rh double relative humidity at the observer (range 0-1)
26793		* @param wl double wavelength (micrometers, Note 9)
26794		*
26795		*<!-- Returned:-->
26796		* @return aob double* <b>Returned</b> observed azimuth (radians: N=0,E=90)
26797		* zob double* <b>Returned</b> observed zenith distance (radians)
26798		* hob double* <b>Returned</b> observed hour angle (radians)
26799		* dob double* <b>Returned</b> observed declination (radians)
26800		* rob double* <b>Returned</b> observed right ascension (CIO-based, radians)
26801		* eo double* <b>Returned</b> equation of the origins (ERA-GST)
26802		*
26803		* @throws JSOFAInternalError
26804		* @throws JSOFAIllegalParameter
26805		* int status: <b>Returned</b> +1 = dubious year (Note 4)
26806		* 0 = <b>Returned</b> OK
26807		* -1 = <b>Returned</b> unacceptable date
26808		*
26809		*<p>Notes:
26810		* <ol>
26811		*
26812		* <li> Star data for an epoch other than J2000.0 (for example from the
26813		* Hipparcos catalog, which has an epoch of J1991.25) will require
26814		* a preliminary call to iauPmsafe before use.
26815		*
26816		* <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
26817		*
26818		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
26819		* convenient way between the two arguments, for example where utc1
26820		* is the Julian Day Number and utc2 is the fraction of a day.
26821		*
26822		* <p>However, JD cannot unambiguously represent UTC during a leap
26823		* second unless special measures are taken. The convention in the
26824		* present function is that the JD day represents UTC days whether
26825		* the length is 86399, 86400 or 86401 SI seconds.
26826		*
26827		* <p>Applications should use the function iauDtf2d to convert from
26828		* calendar date and time of day into 2-part quasi Julian Date, as
26829		* it implements the leap-second-ambiguity convention just
26830		* described.
26831		*
26832		* <li> The warning status "dubious year" flags UTCs that predate the
26833		* introduction of the time scale or that are too far in the
26834		* future to be trusted. See iauDat for further details.
26835		*
26836		* <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
26837		* one second at the end of each positive UTC leap second,
26838		* introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
26839		* practice is under review, and in the future UT1-UTC may grow
26840		* essentially without limit.
26841		*
26842		* <li> The geographical coordinates are with respect to the WGS84
26843		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
26844		* longitude required by the present function is east-positive
26845		* (i.e. right-handed), in accordance with geographical convention.
26846		*
26847		* <li> The polar motion xp,yp can be obtained from IERS bulletins. The
26848		* values are the coordinates (in radians) of the Celestial
26849		* Intermediate Pole with respect to the International Terrestrial
26850		* Reference System (see IERS Conventions 2003), measured along the
26851		* meridians 0 and 90 deg west respectively. For many
26852		* applications, xp and yp can be set to zero.
26853		*
26854		* <li> If hm, the height above the ellipsoid of the observing station
26855		* in meters, is not known but phpa, the pressure in hPa (=mB),
26856		* is available, an adequate estimate of hm can be obtained from
26857		* the expression
26858		*
26859		* <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
26860		*
26861		* <p>where tsl is the approximate sea-level air temperature in K
26862		* (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
26863		* 52). Similarly, if the pressure phpa is not known, it can be
26864		* estimated from the height of the observing station, hm, as
26865		* follows:
26866		*
26867		* <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
26868		*
26869		* <p>Note, however, that the refraction is nearly proportional to
26870		* the pressure and that an accurate phpa value is important for
26871		* precise work.
26872		*
26873		* <li> The argument wl specifies the observing wavelength in
26874		* micrometers. The transition from optical to radio is assumed to
26875		* occur at 100 micrometers (about 3000 GHz).
26876		*
26877		* <li> The accuracy of the result is limited by the corrections for
26878		* refraction, which use a simple Atan(z) + Btan^3(z) model.
26879		* Providing the meteorological parameters are known accurately and
26880		* there are no gross local effects, the predicted observed
26881		* coordinates should be within 0.05 arcsec (optical) or 1 arcsec
26882		* (radio) for a zenith distance of less than 70 degrees, better
26883		* than 30 arcsec (optical or radio) at 85 degrees and better
26884		* than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
26885		*
26886		* <p>Without refraction, the complementary functions iauAtco13 and
26887		* iauAtoc13 are self-consistent to better than 1 microarcsecond
26888		* all over the celestial sphere. With refraction included,
26889		* consistency falls off at high zenith distances, but is still
26890		* better than 0.05 arcsec at 85 degrees.
26891		*
26892		* <li> "Observed" Az,ZD means the position that would be seen by a
26893		* perfect geodetically aligned theodolite. (Zenith distance is
26894		* used rather than altitude in order to reflect the fact that no
26895		* allowance is made for depression of the horizon.) This is
26896		* related to the observed HA,Dec via the standard rotation, using
26897		* the geodetic latitude (corrected for polar motion), while the
26898		* observed HA and RA are related simply through the Earth rotation
26899		* angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
26900		* means the position that would be seen by a perfect equatorial
26901		* with its polar axis aligned to the Earth's axis of rotation.
26902		*
26903		* <li> It is advisable to take great care with units, as even unlikely
26904		* values of the input parameters are accepted and processed in
26905		* accordance with the models used.
26906		*
26907		* </ol>
26908		* Called:
26909		* <ul>
26910		* <li>{@link #jauApco13} astrometry parameters, ICRS-observed, 2013
26911		* <li>{@link #jauAtciq} quick ICRS to CIRS
26912		* <li>{@link #jauAtioq} quick ICRS to observed
26913		*
26914		* </ul>
26915		*@version 2013 October 9
26916		*
26917		*@since JSOFA release 20131202
26918		*
26919		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
26920		* @throws JSOFAInternalError
26921		* @throws JSOFAIllegalParameter
26922		*/
26923		public static ObservedPositionEO jauAtco13(double rc, double dc,
26924		double pr, double pd, double px, double rv,
26925		double utc1, double utc2, double dut1,
26926		double elong, double phi, double hm, double xp, double yp,
26927		double phpa, double tc, double rh, double wl) throws JSOFAIllegalParameter, JSOFAInternalError
26928		{
26929	2	Astrom astrom = new Astrom();
26930
26931
26932		/* Star-independent astrometry parameters. */
26933	2	double eo = jauApco13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
26934		phpa, tc, rh, wl, astrom);
26935
26936		/* Transform ICRS to CIRS. */
26937	2	SphericalCoordinate co = jauAtciq(rc, dc, pr, pd, px, rv, astrom);
26938
26939		/* Transform CIRS to observed. */
26940	2	ObservedPosition obs = jauAtioq(co.alpha, co.delta, astrom);
26941
26942
26943	2	return new ObservedPositionEO(obs, eo);
26944
26945		/* Finished. */
26946
26947
26948		}
26949
26950		/**
26951		* Transform star RA,Dec from geocentric CIRS to ICRS astrometric.
26952		*
26953		*<p>This function is derived from the International Astronomical Union's
26954		* SOFA (Standards of Fundamental Astronomy) software collection.
26955		*
26956		*<p>Status: support function.
26957		*
26958		*<!-- Given: -->
26959		* @param ri double CIRS geocentric RA,Dec (radians)
26960		* @param di double CIRS geocentric RA,Dec (radians)
26961		* @param date1 double TDB as a 2-part...
26962		* @param date2 double ...Julian Date (Note 1)
26963		*
26964		*<!-- Returned:-->
26965		* @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
26966		* eo double <b>Returned</b> equation of the origins (ERA-GST, Note 4)
26967		*
26968		*<p>Notes:
26969		* <ol>
26970		*
26971		* <li> The TDB date date1+date2 is a Julian Date, apportioned in any
26972		* convenient way between the two arguments. For example,
26973		* JD(TDB)=2450123.7 could be expressed in any of these ways, among
26974		* others:
26975		*
26976		* date1 date2
26977		*
26978		* 2450123.7 0.0 (JD method)
26979		* 2451545.0 -1421.3 (J2000 method)
26980		* 2400000.5 50123.2 (MJD method)
26981		* 2450123.5 0.2 (date & time method)
26982		*
26983		* <p>The JD method is the most natural and convenient to use in cases
26984		* where the loss of several decimal digits of resolution is
26985		* acceptable. The J2000 method is best matched to the way the
26986		* argument is handled internally and will deliver the optimum
26987		* resolution. The MJD method and the date & time methods are both
26988		* good compromises between resolution and convenience. For most
26989		* applications of this function the choice will not be at all
26990		* critical.
26991		*
26992		* <p>TT can be used instead of TDB without any significant impact on
26993		* accuracy.
26994		*
26995		* <li> Iterative techniques are used for the aberration and light
26996		* deflection corrections so that the functions iauAtic13 (or
26997		* iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses;
26998		* even at the edge of the Sun's disk the discrepancy is only about
26999		* 1 nanoarcsecond.
27000		*
27001		* <li> The available accuracy is better than 1 milliarcsecond, limited
27002		* mainly by the precession-nutation model that is used, namely
27003		* IAU 2000A/2006. Very close to solar system bodies, additional
27004		* errors of up to several milliarcseconds can occur because of
27005		* unmodeled light deflection; however, the Sun's contribution is
27006		* taken into account, to first order. The accuracy limitations of
27007		* the SOFA function iauEpv00 (used to compute Earth position and
27008		* velocity) can contribute aberration errors of up to
27009		* 5 microarcseconds. Light deflection at the Sun's limb is
27010		* uncertain at the 0.4 mas level.
27011		*
27012		* <li> Should the transformation to (equinox based) J2000.0 mean place
27013		* be required rather than (CIO based) ICRS coordinates, subtract the
27014		* equation of the origins from the returned right ascension:
27015		* RA = RI - EO. (The iauAnp function can then be applied, as
27016		* required, to keep the result in the conventional 0-2pi range.)
27017		*
27018		* </ol>
27019		* Called:
27020		* <ul>
27021		* <li>{@link #jauApci13} astrometry parameters, ICRS-CIRS, 2013
27022		* <li>{@link #jauAticq} quick CIRS to ICRS astrometric
27023		*
27024		* </ul>
27025		*@version 2013 October 9
27026		*
27027		*@since JSOFA release 20131202
27028		*
27029		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27030		*/
27031		public static SphericalCoordinateEO jauAtic13(double ri, double di, double date1, double date2)
27032		{
27033		/* Star-independent astrometry parameters */
27034	2	Astrom astrom = new Astrom();
27035
27036
27037		/* Star-independent astrometry parameters. */
27038	2	double eo = jauApci13(date1, date2, astrom);
27039
27040		/* CIRS to ICRS astrometric. */
27041	2	SphericalCoordinate co = jauAticq(ri, di, astrom);
27042
27043	2	return new SphericalCoordinateEO(co,eo);
27044		/* Finished. */
27045
27046
27047		}
27048
27049		/**
27050		* Quick CIRS RA,Dec to ICRS astrometric place, given the star-
27051		* independent astrometry parameters.
27052		*
27053		* Use of this function is appropriate when efficiency is important and
27054		* where many star positions are all to be transformed for one date.
27055		* The star-independent astrometry parameters can be obtained by
27056		* calling one of the functions iauApci[13], iauApcg[13], iauApco[13]
27057		* or iauApcs[13].
27058		*
27059		*<p>This function is derived from the International Astronomical Union's
27060		* SOFA (Standards of Fundamental Astronomy) software collection.
27061		*
27062		*<p>Status: support function.
27063		*
27064		*<!-- Given: -->
27065		* @param ri double CIRS RA,Dec (radians)
27066		* @param di double CIRS RA,Dec (radians)
27067		* @param astrom star-independent astrometry parameters:
27068		*
27069		*<!-- Returned:-->
27070		* @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
27071		*
27072		*<p>Notes:
27073		* <ol>
27074		*
27075		* <li> Only the Sun is taken into account in the light deflection
27076		* correction.
27077		*
27078		* <li> Iterative techniques are used for the aberration and light
27079		* deflection corrections so that the functions iauAtic13 (or
27080		* iauAticq) and iauAtci13 (or iauAtciq) are accurate inverses;
27081		* even at the edge of the Sun's disk the discrepancy is only about
27082		* 1 nanoarcsecond.
27083		*
27084		* </ol>
27085		* Called:
27086		* <ul>
27087		* <li>{@link #jauS2c} spherical coordinates to unit vector
27088		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
27089		* <li>{@link #jauZp} zero p-vector
27090		* <li>{@link #jauAb} stellar aberration
27091		* <li>{@link #jauLdsun} light deflection by the Sun
27092		* <li>{@link #jauC2s} p-vector to spherical
27093		* <li>{@link #jauAnp} normalize angle into range +/- pi
27094		*
27095		* </ul>
27096		*@version 2013 October 9
27097		*
27098		*@since JSOFA release 20131202
27099		*
27100		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27101		*/
27102		public static SphericalCoordinate jauAticq(double ri, double di, Astrom astrom )
27103		{
27104		int j, i;
27105	10	double pi[] , ppr[], pnat[] = new double[3], pco[] = new double[3], w, d[] = new double[3],
27106	10	before[] = new double[3], r2, r,
27107		after[];
27108
27109
27110		/* CIRS RA,Dec to Cartesian. */
27111	10	pi = jauS2c(ri, di);
27112
27113		/* Bias-precession-nutation, giving GCRS proper direction. */
27114	10	ppr = jauTrxp(astrom.bpn, pi);
27115
27116		/* Aberration, giving GCRS natural direction. */
27117	10	jauZp(d);
27118	30	for (j = 0; j < 2; j++) {
27119	20	r2 = 0.0;
27120	80	for (i = 0; i < 3; i++) {
27121	60	w = ppr[i] - d[i];
27122	60	before[i] = w;
27123	60	r2 += w*w;
27124		}
27125	20	r = sqrt(r2);
27126	80	for (i = 0; i < 3; i++) {
27127	60	before[i] /= r;
27128		}
27129	20	after = jauAb(before, astrom.v, astrom.em, astrom.bm1);
27130	20	r2 = 0.0;
27131	80	for (i = 0; i < 3; i++) {
27132	60	d[i] = after[i] - before[i];
27133	60	w = ppr[i] - d[i];
27134	60	pnat[i] = w;
27135	60	r2 += w*w;
27136		}
27137	20	r = sqrt(r2);
27138	80	for (i = 0; i < 3; i++) {
27139	60	pnat[i] /= r;
27140		}
27141		}
27142
27143		/* Light deflection by the Sun, giving BCRS coordinate direction. */
27144	10	jauZp(d);
27145	60	for (j = 0; j < 5; j++) {
27146	50	r2 = 0.0;
27147	200	for (i = 0; i < 3; i++) {
27148	150	w = pnat[i] - d[i];
27149	150	before[i] = w;
27150	150	r2 += w*w;
27151		}
27152	50	r = sqrt(r2);
27153	200	for (i = 0; i < 3; i++) {
27154	150	before[i] /= r;
27155		}
27156	50	after = jauLdsun(before, astrom.eh, astrom.em);
27157	50	r2 = 0.0;
27158	200	for (i = 0; i < 3; i++) {
27159	150	d[i] = after[i] - before[i];
27160	150	w = pnat[i] - d[i];
27161	150	pco[i] = w;
27162	150	r2 += w*w;
27163		}
27164	50	r = sqrt(r2);
27165	200	for (i = 0; i < 3; i++) {
27166	150	pco[i] /= r;
27167		}
27168		}
27169
27170		/* ICRS astrometric RA,Dec. */
27171	10	SphericalCoordinate co = jauC2s(pco);
27172	10	co.alpha = jauAnp(co.alpha);
27173
27174	10	return co;
27175		/* Finished. */
27176
27177
27178		}
27179
27180		/**
27181		* Quick CIRS to ICRS astrometric place transformation, given the star-
27182		* independent astrometry parameters plus a list of light-deflecting
27183		* bodies.
27184		*
27185		* Use of this function is appropriate when efficiency is important and
27186		* where many star positions are all to be transformed for one date.
27187		* The star-independent astrometry parameters can be obtained by
27188		* calling one of the functions iauApci[13], iauApcg[13], iauApco[13]
27189		* or iauApcs[13].
27190		*
27191		* If the only light-deflecting body to be taken into account is the
27192		* Sun, the iauAticq function can be used instead.
27193		*
27194		*<p>This function is derived from the International Astronomical Union's
27195		* SOFA (Standards of Fundamental Astronomy) software collection.
27196		*
27197		*<p>Status: support function.
27198		*
27199		*<!-- Given: -->
27200		* @param ri double CIRS RA,Dec (radians)
27201		* @param di double CIRS RA,Dec (radians)
27202		* @param astrom star-independent astrometry parameters:
27203		*
27204		*<!-- Returned:-->
27205		* @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
27206		*
27207		*<p>Notes:
27208		* <ol>
27209		*
27210		* <li> Iterative techniques are used for the aberration and light
27211		* deflection corrections so that the functions iauAticqn and
27212		* iauAtciqn are accurate inverses; even at the edge of the Sun's
27213		* disk the discrepancy is only about 1 nanoarcsecond.
27214		*
27215		* <li> If the only light-deflecting body to be taken into account is the
27216		* Sun, the iauAticq function can be used instead.
27217		*
27218		* <li> The struct b contains n entries, one for each body to be
27219		* considered. If n = 0, no gravitational light deflection will be
27220		* applied, not even for the Sun.
27221		*
27222		* <li> The struct b should include an entry for the Sun as well as for
27223		* any planet or other body to be taken into account. The entries
27224		* should be in the order in which the light passes the body.
27225		*
27226		* <li> In the entry in the b struct for body i, the mass parameter
27227		* b[i].bm can, as required, be adjusted in order to allow for such
27228		* effects as quadrupole field.
27229		*
27230		* <li> The deflection limiter parameter b[i].dl is phi^2/2, where phi is
27231		* the angular separation (in radians) between star and body at
27232		* which limiting is applied. As phi shrinks below the chosen
27233		* threshold, the deflection is artificially reduced, reaching zero
27234		* for phi = 0. Example values suitable for a terrestrial
27235		* observer, together with masses, are as follows:
27236		*
27237		* <p>body i b[i].bm b[i].dl
27238		*
27239		* <p>Sun 1.0 6e-6
27240		* Jupiter 0.00095435 3e-9
27241		* Saturn 0.00028574 3e-10
27242		*
27243		* <li> For efficiency, validation of the contents of the b array is
27244		* omitted. The supplied masses must be greater than zero, the
27245		* position and velocity vectors must be right, and the deflection
27246		* limiter greater than zero.
27247		*
27248		* </ol>
27249		* Called:
27250		* <ul>
27251		* <li>{@link #jauS2c} spherical coordinates to unit vector
27252		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
27253		* <li>{@link #jauZp} zero p-vector
27254		* <li>{@link #jauAb} stellar aberration
27255		* <li>{@link #jauLdn} light deflection by n bodies
27256		* <li>{@link #jauC2s} p-vector to spherical
27257		* <li>{@link #jauAnp} normalize angle into range +/- pi
27258		*
27259		* </ul>
27260		*@version 2013 October 9
27261		*
27262		*@since JSOFA release 20131202
27263		*
27264		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27265		*/
27266		public static SphericalCoordinate jauAticqn(double ri, double di, Astrom astrom,
27267		int n, Ldbody b[])
27268		{
27269		int j, i;
27270	2	double pi[], ppr[], pnat[] = new double[3], pco[] = new double[3], w, d[] = new double[3], before[] = new double[3], r2, r,
27271		after[];
27272
27273
27274		/* CIRS RA,Dec to Cartesian. */
27275	2	pi = jauS2c(ri, di);
27276
27277		/* Bias-precession-nutation, giving GCRS proper direction. */
27278	2	ppr = jauTrxp(astrom.bpn, pi);
27279
27280		/* Aberration, giving GCRS natural direction. */
27281	2	jauZp(d);
27282	6	for (j = 0; j < 2; j++) {
27283	4	r2 = 0.0;
27284	16	for (i = 0; i < 3; i++) {
27285	12	w = ppr[i] - d[i];
27286	12	before[i] = w;
27287	12	r2 += w*w;
27288		}
27289	4	r = sqrt(r2);
27290	16	for (i = 0; i < 3; i++) {
27291	12	before[i] /= r;
27292		}
27293	4	after = jauAb(before, astrom.v, astrom.em, astrom.bm1);
27294	4	r2 = 0.0;
27295	16	for (i = 0; i < 3; i++) {
27296	12	d[i] = after[i] - before[i];
27297	12	w = ppr[i] - d[i];
27298	12	pnat[i] = w;
27299	12	r2 += w*w;
27300		}
27301	4	r = sqrt(r2);
27302	16	for (i = 0; i < 3; i++) {
27303	12	pnat[i] /= r;
27304		}
27305		}
27306
27307		/* Light deflection, giving BCRS coordinate direction. */
27308	2	jauZp(d);
27309	12	for (j = 0; j < 5; j++) {
27310	10	r2 = 0.0;
27311	40	for (i = 0; i < 3; i++) {
27312	30	w = pnat[i] - d[i];
27313	30	before[i] = w;
27314	30	r2 += w*w;
27315		}
27316	10	r = sqrt(r2);
27317	40	for (i = 0; i < 3; i++) {
27318	30	before[i] /= r;
27319		}
27320	10	after = jauLdn(n, b, astrom.eb, before);
27321	10	r2 = 0.0;
27322	40	for (i = 0; i < 3; i++) {
27323	30	d[i] = after[i] - before[i];
27324	30	w = pnat[i] - d[i];
27325	30	pco[i] = w;
27326	30	r2 += w*w;
27327		}
27328	10	r = sqrt(r2);
27329	40	for (i = 0; i < 3; i++) {
27330	30	pco[i] /= r;
27331		}
27332		}
27333
27334		/* ICRS astrometric RA,Dec. */
27335	2	SphericalCoordinate co = jauC2s(pco);
27336	2	co.alpha = jauAnp(co.alpha);
27337
27338	2	return co;
27339		/* Finished. */
27340
27341
27342		}
27343
27344		/**
27345		* Observed Position.
27346		* "Observed" Az,ZD means the position that would be seen by a
27347		* perfect geodetically aligned theodolite. (Zenith distance is
27348		* used rather than altitude in order to reflect the fact that no
27349		* allowance is made for depression of the horizon.) This is
27350		* related to the observed HA,Dec via the standard rotation, using
27351		* the geodetic latitude (corrected for polar motion), while the
27352		* observed HA and RA are related simply through the Earth rotation
27353		* angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27354		* means the position that would be seen by a perfect equatorial
27355		* with its polar axis aligned to the Earth's axis of rotation..
27356		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Mar 2014
27357		* @version $Revision$ $date$
27358		*/
27359		public static class ObservedPosition{
27360		/** observed azimuth (radians: N=0,E=90) */
27361		public double aob;
27362
27363		/** observed zenith distance (radians) */
27364		public double zob;
27365
27366		/** observed Hour Angle (radians) */
27367		public double hob;
27368
27369		/** observed Declination (radians) */
27370		public double dob;
27371
27372		/** observed Right Ascension (radians) */
27373		public double rob;
27374		public ObservedPosition(double aob,
27375		double zob,
27376		double hob,
27377		double dob,
27378		double rob
27379	6	) {
27380	6	this.aob = aob;
27381	6	this.zob = zob;
27382	6	this.hob = hob;
27383	6	this.dob = dob;
27384	6	this.rob = rob;
27385	6	}
27386		}
27387
27388		/**
27389		* Observed position with the equation of the origins.
27390		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 29 Mar 2014
27391		* @version $Revision$ $date$
27392		*/
27393		public static class ObservedPositionEO {
27394		/**
27395		* observed position.
27396		*/
27397		public ObservedPosition op;
27398		/**
27399		* The equation of the origins. The equation of the origins is the distance between the true
27400		* equinox and the celestial intermediate origin and, equivalently,
27401		* the difference between Earth rotation angle and Greenwich
27402		* apparent sidereal time (ERA-GST). It comprises the precession
27403		* (since J2000.0) in right ascension plus the equation of the
27404		* equinoxes (including the small correction terms).
27405		*/
27406		public double eo;
27407		/**
27408		* @param op
27409		* @param eo
27410		*/
27411	2	public ObservedPositionEO(ObservedPosition op, double eo) {
27412	2	this.op = op;
27413	2	this.eo = eo;
27414	2	}
27415
27416		}
27417
27418
27419
27420
27421		/**
27422		* CIRS RA,Dec to observed place. The caller supplies UTC, site
27423		* coordinates, ambient air conditions and observing wavelength.
27424		*
27425		*<p>This function is derived from the International Astronomical Union's
27426		* SOFA (Standards of Fundamental Astronomy) software collection.
27427		*
27428		*<p>Status: support function.
27429		*
27430		*<!-- Given: -->
27431		* @param ri double CIRS right ascension (CIO-based, radians)
27432		* @param di double CIRS declination (radians)
27433		* @param utc1 double UTC as a 2-part...
27434		* @param utc2 double ...quasi Julian Date (Notes 1,2)
27435		* @param dut1 double UT1-UTC (seconds, Note 3)
27436		* @param elong double longitude (radians, east +ve, Note 4)
27437		* @param phi double geodetic latitude (radians, Note 4)
27438		* @param hm double height above ellipsoid (m, geodetic Notes 4,6)
27439		* @param xp double polar motion coordinates (radians, Note 5)
27440		* @param yp double polar motion coordinates (radians, Note 5)
27441		* @param phpa double pressure at the observer (hPa = mB, Note 6)
27442		* @param tc double ambient temperature at the observer (deg C)
27443		* @param rh double relative humidity at the observer (range 0-1)
27444		* @param wl double wavelength (micrometers, Note 7)
27445		*
27446		*<!-- Returned:-->
27447		* @return aob double* <b>Returned</b> observed azimuth (radians: N=0,E=90)
27448		* zob double* <b>Returned</b> observed zenith distance (radians)
27449		* hob double* <b>Returned</b> observed hour angle (radians)
27450		* dob double* <b>Returned</b> observed declination (radians)
27451		* rob double* <b>Returned</b> observed right ascension (CIO-based, radians)
27452		*
27453		* @throws JSOFAInternalError
27454		* @throws JSOFAIllegalParameter
27455		* int status: <b>Returned</b> +1 = dubious year (Note 2)
27456		* 0 = <b>Returned</b> OK
27457		* -1 = <b>Returned</b> unacceptable date
27458		*
27459		*<p>Notes:
27460		* <ol>
27461		*
27462		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
27463		* convenient way between the two arguments, for example where utc1
27464		* is the Julian Day Number and utc2 is the fraction of a day.
27465		*
27466		* <p>However, JD cannot unambiguously represent UTC during a leap
27467		* second unless special measures are taken. The convention in the
27468		* present function is that the JD day represents UTC days whether
27469		* the length is 86399, 86400 or 86401 SI seconds.
27470		*
27471		* <p>Applications should use the function iauDtf2d to convert from
27472		* calendar date and time of day into 2-part quasi Julian Date, as
27473		* it implements the leap-second-ambiguity convention just
27474		* described.
27475		*
27476		* <li> The warning status "dubious year" flags UTCs that predate the
27477		* introduction of the time scale or that are too far in the
27478		* future to be trusted. See iauDat for further details.
27479		*
27480		* <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
27481		* one second at the end of each positive UTC leap second,
27482		* introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
27483		* practice is under review, and in the future UT1-UTC may grow
27484		* essentially without limit.
27485		*
27486		* <li> The geographical coordinates are with respect to the WGS84
27487		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
27488		* longitude required by the present function is east-positive
27489		* (i.e. right-handed), in accordance with geographical convention.
27490		*
27491		* <li> The polar motion xp,yp can be obtained from IERS bulletins. The
27492		* values are the coordinates (in radians) of the Celestial
27493		* Intermediate Pole with respect to the International Terrestrial
27494		* Reference System (see IERS Conventions 2003), measured along the
27495		* meridians 0 and 90 deg west respectively. For many
27496		* applications, xp and yp can be set to zero.
27497		*
27498		* <li> If hm, the height above the ellipsoid of the observing station
27499		* in meters, is not known but phpa, the pressure in hPa (=mB), is
27500		* available, an adequate estimate of hm can be obtained from the
27501		* expression
27502		*
27503		* <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
27504		*
27505		* <p>where tsl is the approximate sea-level air temperature in K
27506		* (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
27507		* 52). Similarly, if the pressure phpa is not known, it can be
27508		* estimated from the height of the observing station, hm, as
27509		* follows:
27510		*
27511		* <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
27512		*
27513		* <p>Note, however, that the refraction is nearly proportional to
27514		* the pressure and that an accurate phpa value is important for
27515		* precise work.
27516		*
27517		* <li> The argument wl specifies the observing wavelength in
27518		* micrometers. The transition from optical to radio is assumed to
27519		* occur at 100 micrometers (about 3000 GHz).
27520		*
27521		* <li> "Observed" Az,ZD means the position that would be seen by a
27522		* perfect geodetically aligned theodolite. (Zenith distance is
27523		* used rather than altitude in order to reflect the fact that no
27524		* allowance is made for depression of the horizon.) This is
27525		* related to the observed HA,Dec via the standard rotation, using
27526		* the geodetic latitude (corrected for polar motion), while the
27527		* observed HA and RA are related simply through the Earth rotation
27528		* angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27529		* means the position that would be seen by a perfect equatorial
27530		* with its polar axis aligned to the Earth's axis of rotation.
27531		*
27532		* <li> The accuracy of the result is limited by the corrections for
27533		* refraction, which use a simple Atan(z) + Btan^3(z) model.
27534		* Providing the meteorological parameters are known accurately and
27535		* there are no gross local effects, the predicted astrometric
27536		* coordinates should be within 0.05 arcsec (optical) or 1 arcsec
27537		* (radio) for a zenith distance of less than 70 degrees, better
27538		* than 30 arcsec (optical or radio) at 85 degrees and better
27539		* than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
27540		*
27541		* <li> The complementary functions iauAtio13 and iauAtoi13 are self-
27542		* consistent to better than 1 microarcsecond all over the
27543		* celestial sphere.
27544		*
27545		* <li> It is advisable to take great care with units, as even unlikely
27546		* values of the input parameters are accepted and processed in
27547		* accordance with the models used.
27548		*
27549		* </ol>
27550		* Called:
27551		* <ul>
27552		* <li>{@link #jauApio13} astrometry parameters, CIRS-observed, 2013
27553		* <li>{@link #jauAtioq} quick CIRS to observed
27554		*
27555		* </ul>
27556		*@version 2013 October 9
27557		*
27558		*@since JSOFA release 20131202
27559		*
27560		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27561		* @throws JSOFAInternalError
27562		* @throws JSOFAIllegalParameter
27563		*/
27564		public static ObservedPosition jauAtio13(double ri, double di,
27565		double utc1, double utc2, double dut1,
27566		double elong, double phi, double hm, double xp, double yp,
27567		double phpa, double tc, double rh, double wl) throws JSOFAIllegalParameter, JSOFAInternalError
27568		{
27569	2	Astrom astrom = new Astrom();
27570
27571
27572		/* Star-independent astrometry parameters for CIRS->observed. */
27573	2	jauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
27574		phpa, tc, rh, wl, astrom);
27575
27576		/* Transform CIRS to observed. */
27577	2	return jauAtioq(ri, di, astrom);
27578
27579		/* Finished. */
27580
27581
27582		}
27583
27584		/**
27585		* Quick CIRS to observed place transformation.
27586		*
27587		* Use of this function is appropriate when efficiency is important and
27588		* where many star positions are all to be transformed for one date.
27589		* The star-independent astrometry parameters can be obtained by
27590		* calling iauApio[13] or iauApco[13].
27591		*
27592		*<p>This function is derived from the International Astronomical Union's
27593		* SOFA (Standards of Fundamental Astronomy) software collection.
27594		*
27595		*<p>Status: support function.
27596		*
27597		*<!-- Given: -->
27598		* @param ri double CIRS right ascension
27599		* @param di double CIRS declination
27600		* @param astrom star-independent astrometry parameters:
27601		*
27602		*<!-- Returned:-->
27603		* @return aob double* <b>Returned</b> observed azimuth (radians: N=0,E=90)
27604		* zob double* <b>Returned</b> observed zenith distance (radians)
27605		* hob double* <b>Returned</b> observed hour angle (radians)
27606		* dob double* <b>Returned</b> observed declination (radians)
27607		* rob double* <b>Returned</b> observed right ascension (CIO-based, radians)
27608		*
27609		*<p>Notes:
27610		* <ol>
27611		*
27612		* <li> This function returns zenith distance rather than altitude in
27613		* order to reflect the fact that no allowance is made for
27614		* depression of the horizon.
27615		*
27616		* <li> The accuracy of the result is limited by the corrections for
27617		* refraction, which use a simple Atan(z) + Btan^3(z) model.
27618		* Providing the meteorological parameters are known accurately and
27619		* there are no gross local effects, the predicted observed
27620		* coordinates should be within 0.05 arcsec (optical) or 1 arcsec
27621		* (radio) for a zenith distance of less than 70 degrees, better
27622		* than 30 arcsec (optical or radio) at 85 degrees and better
27623		* than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
27624		*
27625		* <p>Without refraction, the complementary functions iauAtioq and
27626		* iauAtoiq are self-consistent to better than 1 microarcsecond all
27627		* over the celestial sphere. With refraction included, consistency
27628		* falls off at high zenith distances, but is still better than
27629		* 0.05 arcsec at 85 degrees.
27630		*
27631		* <li> It is advisable to take great care with units, as even unlikely
27632		* values of the input parameters are accepted and processed in
27633		* accordance with the models used.
27634		*
27635		* <li> The CIRS RA,Dec is obtained from a star catalog mean place by
27636		* allowing for space motion, parallax, the Sun's gravitational lens
27637		* effect, annual aberration and precession-nutation. For star
27638		* positions in the ICRS, these effects can be applied by means of
27639		* the iauAtci13 (etc.) functions. Starting from classical "mean
27640		* place" systems, additional transformations will be needed first.
27641		*
27642		* <li> "Observed" Az,El means the position that would be seen by a
27643		* perfect geodetically aligned theodolite. This is obtained from
27644		* the CIRS RA,Dec by allowing for Earth orientation and diurnal
27645		* aberration, rotating from equator to horizon coordinates, and
27646		* then adjusting for refraction. The HA,Dec is obtained by
27647		* rotating back into equatorial coordinates, and is the position
27648		* that would be seen by a perfect equatorial with its polar axis
27649		* aligned to the Earth's axis of rotation. Finally, the RA is
27650		* obtained by subtracting the HA from the local ERA.
27651		*
27652		* <li> The star-independent CIRS-to-observed-place parameters in ASTROM
27653		* may be computed with iauApio[13] or iauApco[13]. If nothing has
27654		* changed significantly except the time, iauAper[13] may be used to
27655		* perform the requisite adjustment to the astrom structure.
27656		*
27657		* </ol>
27658		* Called:
27659		* <ul>
27660		* <li>{@link #jauS2c} spherical coordinates to unit vector
27661		* <li>{@link #jauC2s} p-vector to spherical
27662		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
27663		*
27664		* </ul>
27665		*@version 2013 December 5
27666		*
27667		*@since JSOFA release 20131202
27668		*
27669		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27670		*/
27671		public static ObservedPosition jauAtioq(double ri, double di, Astrom astrom)
27672		{
27673		/* Minimum cos(alt) and sin(alt) for refraction purposes */
27674	6	final double CELMIN = 1e-6;
27675	6	final double SELMIN = 0.05;
27676
27677	6	double v[] = new double[3], x, y, z, xhd, yhd, zhd, f, xhdt, yhdt, zhdt,
27678		xaet, yaet, zaet, azobs, r, tz, w, del, cosdel,
27679		xaeo, yaeo, zaeo, zdobs, hmobs, dcobs, raobs;
27680
27681		/--------------------------------------------------------------------/
27682
27683		/* CIRS RA,Dec to Cartesian -HA,Dec. */
27684	6	v = jauS2c(ri-astrom.eral, di);
27685	6	x = v[0];
27686	6	y = v[1];
27687	6	z = v[2];
27688
27689		/* Polar motion. */
27690	6	xhd = x + astrom.xpl*z;
27691	6	yhd = y - astrom.ypl*z;
27692	6	zhd = z - astrom.xplx + astrom.yply;
27693
27694		/* Diurnal aberration. */
27695	6	f = ( 1.0 - astrom.diurab*yhd );
27696	6	xhdt = f * xhd;
27697	6	yhdt = f * ( yhd + astrom.diurab );
27698	6	zhdt = f * zhd;
27699
27700		/* Cartesian -HA,Dec to Cartesian Az,El (S=0,E=90). */
27701	6	xaet = astrom.sphixhdt - astrom.cphizhdt;
27702	6	yaet = yhdt;
27703	6	zaet = astrom.cphixhdt + astrom.sphizhdt;
27704
27705		/* Azimuth (N=0,E=90). */
27706	6	azobs = ( xaet != 0.0 \|\| yaet != 0.0 ) ? atan2(yaet,-xaet) : 0.0;
27707
27708		/* ---------- */
27709		/* Refraction */
27710		/* ---------- */
27711
27712		/* Cosine and sine of altitude, with precautions. */
27713	6	r = sqrt(xaetxaet + yaetyaet);
27714	6	r = r > CELMIN ? r : CELMIN;
27715	6	z = zaet > SELMIN ? zaet : SELMIN;
27716
27717		/* Atan(z)+Btan^3(z) model, with Newton-Raphson correction. */
27718	6	tz = r/z;
27719	6	w = astrom.refbtztz;
27720	6	del = ( astrom.refa + w ) * tz /
27721		( 1.0 + ( astrom.refa + 3.0w ) / ( zz ) );
27722
27723		/* Apply the change, giving observed vector. */
27724	6	cosdel = 1.0 - del*del/2.0;
27725	6	f = cosdel - del*z/r;
27726	6	xaeo = xaet*f;
27727	6	yaeo = yaet*f;
27728	6	zaeo = cosdelzaet + delr;
27729
27730		/* Observed ZD. */
27731	6	zdobs = atan2(sqrt(xaeoxaeo+yaeoyaeo), zaeo);
27732
27733		/* Az/El vector to HA,Dec vector (both right-handed). */
27734	6	v[0] = astrom.sphixaeo + astrom.cphizaeo;
27735	6	v[1] = yaeo;
27736	6	v[2] = - astrom.cphixaeo + astrom.sphizaeo;
27737
27738		/* To spherical -HA,Dec. */
27739	6	SphericalCoordinate co = jauC2s ( v);
27740	6	hmobs = co.alpha;
27741	6	dcobs = co.delta;
27742		/* Right ascension (with respect to CIO). */
27743	6	raobs = astrom.eral + hmobs;
27744
27745		/* Return the results. */
27746	6	return new ObservedPosition(
27747	6	jauAnp(azobs),
27748		zdobs,
27749		-hmobs,
27750		dcobs,
27751	6	jauAnp(raobs));
27752
27753		/* Finished. */
27754
27755
27756		}
27757
27758		/**
27759		* Observed place at a groundbased site to to ICRS astrometric RA,Dec.
27760		* The caller supplies UTC, site coordinates, ambient air conditions
27761		* and observing wavelength.
27762		*
27763		*<p>This function is derived from the International Astronomical Union's
27764		* SOFA (Standards of Fundamental Astronomy) software collection.
27765		*
27766		*<p>Status: support function.
27767		*
27768		*<!-- Given: -->
27769		* @param type char[] type of coordinates - "R", "H" or "A" (Notes 1,2)
27770		* @param ob1 double observed Az, HA or RA (radians; Az is N=0,E=90)
27771		* @param ob2 double observed ZD or Dec (radians)
27772		* @param utc1 double UTC as a 2-part...
27773		* @param utc2 double ...quasi Julian Date (Notes 3,4)
27774		* @param dut1 double UT1-UTC (seconds, Note 5)
27775		* @param elong double longitude (radians, east +ve, Note 6)
27776		* @param phi double geodetic latitude (radians, Note 6)
27777		* @param hm double height above ellipsoid (m, geodetic Notes 6,8)
27778		* @param xp double polar motion coordinates (radians, Note 7)
27779		* @param yp double polar motion coordinates (radians, Note 7)
27780		* @param phpa double pressure at the observer (hPa = mB, Note 8)
27781		* @param tc double ambient temperature at the observer (deg C)
27782		* @param rh double relative humidity at the observer (range 0-1)
27783		* @param wl double wavelength (micrometers, Note 9)
27784		*
27785		*<!-- Returned:-->
27786		* @return rc,dc double <b>Returned</b> ICRS astrometric RA,Dec (radians)
27787		*
27788		* @throws JSOFAInternalError
27789		* @throws JSOFAIllegalParameter
27790		* int status: <b>Returned</b> +1 = dubious year (Note 4)
27791		* 0 = <b>Returned</b> OK
27792		* -1 = <b>Returned</b> unacceptable date
27793		*
27794		*<p>Notes:
27795		* <ol>
27796		*
27797		* <li> "Observed" Az,ZD means the position that would be seen by a
27798		* perfect geodetically aligned theodolite. (Zenith distance is
27799		* used rather than altitude in order to reflect the fact that no
27800		* allowance is made for depression of the horizon.) This is
27801		* related to the observed HA,Dec via the standard rotation, using
27802		* the geodetic latitude (corrected for polar motion), while the
27803		* observed HA and RA are related simply through the Earth rotation
27804		* angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27805		* means the position that would be seen by a perfect equatorial
27806		* with its polar axis aligned to the Earth's axis of rotation.
27807		*
27808		* <li> Only the first character of the type argument is significant.
27809		* "R" or "r" indicates that ob1 and ob2 are the observed right
27810		* ascension and declination; "H" or "h" indicates that they are
27811		* hour angle (west +ve) and declination; anything else ("A" or
27812		* "a" is recommended) indicates that ob1 and ob2 are azimuth
27813		* (north zero, east 90 deg) and zenith distance.
27814		*
27815		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
27816		* convenient way between the two arguments, for example where utc1
27817		* is the Julian Day Number and utc2 is the fraction of a day.
27818		*
27819		* <p>However, JD cannot unambiguously represent UTC during a leap
27820		* second unless special measures are taken. The convention in the
27821		* present function is that the JD day represents UTC days whether
27822		* the length is 86399, 86400 or 86401 SI seconds.
27823		*
27824		* <p>Applications should use the function iauDtf2d to convert from
27825		* calendar date and time of day into 2-part quasi Julian Date, as
27826		* it implements the leap-second-ambiguity convention just
27827		* described.
27828		*
27829		* <li> The warning status "dubious year" flags UTCs that predate the
27830		* introduction of the time scale or that are too far in the
27831		* future to be trusted. See iauDat for further details.
27832		*
27833		* <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
27834		* one second at the end of each positive UTC leap second,
27835		* introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
27836		* practice is under review, and in the future UT1-UTC may grow
27837		* essentially without limit.
27838		*
27839		* <li> The geographical coordinates are with respect to the WGS84
27840		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
27841		* longitude required by the present function is east-positive
27842		* (i.e. right-handed), in accordance with geographical convention.
27843		*
27844		* <li> The polar motion xp,yp can be obtained from IERS bulletins. The
27845		* values are the coordinates (in radians) of the Celestial
27846		* Intermediate Pole with respect to the International Terrestrial
27847		* Reference System (see IERS Conventions 2003), measured along the
27848		* meridians 0 and 90 deg west respectively. For many
27849		* applications, xp and yp can be set to zero.
27850		*
27851		* <li> If hm, the height above the ellipsoid of the observing station
27852		* in meters, is not known but phpa, the pressure in hPa (=mB), is
27853		* available, an adequate estimate of hm can be obtained from the
27854		* expression
27855		*
27856		* <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
27857		*
27858		* <p>where tsl is the approximate sea-level air temperature in K
27859		* (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
27860		* 52). Similarly, if the pressure phpa is not known, it can be
27861		* estimated from the height of the observing station, hm, as
27862		* follows:
27863		*
27864		* <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
27865		*
27866		* <p>Note, however, that the refraction is nearly proportional to
27867		* the pressure and that an accurate phpa value is important for
27868		* precise work.
27869		*
27870		* <li> The argument wl specifies the observing wavelength in
27871		* micrometers. The transition from optical to radio is assumed to
27872		* occur at 100 micrometers (about 3000 GHz).
27873		*
27874		* <li> The accuracy of the result is limited by the corrections for
27875		* refraction, which use a simple Atan(z) + Btan^3(z) model.
27876		* Providing the meteorological parameters are known accurately and
27877		* there are no gross local effects, the predicted astrometric
27878		* coordinates should be within 0.05 arcsec (optical) or 1 arcsec
27879		* (radio) for a zenith distance of less than 70 degrees, better
27880		* than 30 arcsec (optical or radio) at 85 degrees and better
27881		* than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
27882		*
27883		* <p>Without refraction, the complementary functions iauAtco13 and
27884		* iauAtoc13 are self-consistent to better than 1 microarcsecond
27885		* all over the celestial sphere. With refraction included,
27886		* consistency falls off at high zenith distances, but is still
27887		* better than 0.05 arcsec at 85 degrees.
27888		*
27889		* <li> It is advisable to take great care with units, as even unlikely
27890		* values of the input parameters are accepted and processed in
27891		* accordance with the models used.
27892		*
27893		* </ol>
27894		* Called:
27895		* <ul>
27896		* <li>{@link #jauApco13} astrometry parameters, ICRS-observed
27897		* <li>{@link #jauAtoiq} quick observed to CIRS
27898		* <li>{@link #jauAticq} quick CIRS to ICRS
27899		*
27900		* </ul>
27901		*@version 2013 October 9
27902		*
27903		*@since JSOFA release 20131202
27904		*
27905		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
27906		* @throws JSOFAInternalError
27907		* @throws JSOFAIllegalParameter
27908		*/
27909		public static SphericalCoordinate jauAtoc13(String type, double ob1, double ob2,
27910		double utc1, double utc2, double dut1,
27911		double elong, double phi, double hm, double xp, double yp,
27912		double phpa, double tc, double rh, double wl
27913		) throws JSOFAIllegalParameter, JSOFAInternalError
27914		{
27915	6	Astrom astrom = new Astrom();
27916	6	jauApco13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
27917		phpa, tc, rh, wl, astrom);
27918
27919		/* Transform observed to CIRS. */
27920	6	SphericalCoordinate co = jauAtoiq(type, ob1, ob2, astrom);
27921
27922		/* Transform CIRS to ICRS. */
27923	6	SphericalCoordinate icrs = jauAticq(co.alpha, co.delta, astrom);
27924	6	return icrs;
27925
27926
27927		/* Finished. */
27928
27929
27930		}
27931
27932		/**
27933		* Observed place to CIRS. The caller supplies UTC, site coordinates,
27934		* ambient air conditions and observing wavelength.
27935		*
27936		*<p>This function is derived from the International Astronomical Union's
27937		* SOFA (Standards of Fundamental Astronomy) software collection.
27938		*
27939		*<p>Status: support function.
27940		*
27941		*<!-- Given: -->
27942		* @param type char[] type of coordinates - "R", "H" or "A" (Notes 1,2)
27943		* @param ob1 double observed Az, HA or RA (radians; Az is N=0,E=90)
27944		* @param ob2 double observed ZD or Dec (radians)
27945		* @param utc1 double UTC as a 2-part...
27946		* @param utc2 double ...quasi Julian Date (Notes 3,4)
27947		* @param dut1 double UT1-UTC (seconds, Note 5)
27948		* @param elong double longitude (radians, east +ve, Note 6)
27949		* @param phi double geodetic latitude (radians, Note 6)
27950		* @param hm double height above the ellipsoid (meters, Notes 6,8)
27951		* @param xp double polar motion coordinates (radians, Note 7)
27952		* @param yp double polar motion coordinates (radians, Note 7)
27953		* @param phpa double pressure at the observer (hPa = mB, Note 8)
27954		* @param tc double ambient temperature at the observer (deg C)
27955		* @param rh double relative humidity at the observer (range 0-1)
27956		* @param wl double wavelength (micrometers, Note 9)
27957		*
27958		*<!-- Returned:-->
27959		* @return ri double* <b>Returned</b> CIRS right ascension (CIO-based, radians)
27960		* di double* <b>Returned</b> CIRS declination (radians)
27961		*
27962		* @throws JSOFAInternalError
27963		* @throws JSOFAIllegalParameter
27964		* int status: <b>Returned</b> +1 = dubious year (Note 2)
27965		* 0 = <b>Returned</b> OK
27966		* -1 = <b>Returned</b> unacceptable date
27967		*
27968		*<p>Notes:
27969		* <ol>
27970		*
27971		* <li> "Observed" Az,ZD means the position that would be seen by a
27972		* perfect geodetically aligned theodolite. (Zenith distance is
27973		* used rather than altitude in order to reflect the fact that no
27974		* allowance is made for depression of the horizon.) This is
27975		* related to the observed HA,Dec via the standard rotation, using
27976		* the geodetic latitude (corrected for polar motion), while the
27977		* observed HA and RA are related simply through the Earth rotation
27978		* angle and the site longitude. "Observed" RA,Dec or HA,Dec thus
27979		* means the position that would be seen by a perfect equatorial
27980		* with its polar axis aligned to the Earth's axis of rotation.
27981		*
27982		* <li> Only the first character of the type argument is significant.
27983		* "R" or "r" indicates that ob1 and ob2 are the observed right
27984		* ascension and declination; "H" or "h" indicates that they are
27985		* hour angle (west +ve) and declination; anything else ("A" or
27986		* "a" is recommended) indicates that ob1 and ob2 are azimuth
27987		* (north zero, east 90 deg) and zenith distance.
27988		*
27989		* <li> utc1+utc2 is quasi Julian Date (see Note 2), apportioned in any
27990		* convenient way between the two arguments, for example where utc1
27991		* is the Julian Day Number and utc2 is the fraction of a day.
27992		*
27993		* <p>However, JD cannot unambiguously represent UTC during a leap
27994		* second unless special measures are taken. The convention in the
27995		* present function is that the JD day represents UTC days whether
27996		* the length is 86399, 86400 or 86401 SI seconds.
27997		*
27998		* <p>Applications should use the function iauDtf2d to convert from
27999		* calendar date and time of day into 2-part quasi Julian Date, as
28000		* it implements the leap-second-ambiguity convention just
28001		* described.
28002		*
28003		* <li> The warning status "dubious year" flags UTCs that predate the
28004		* introduction of the time scale or that are too far in the
28005		* future to be trusted. See iauDat for further details.
28006		*
28007		* <li> UT1-UTC is tabulated in IERS bulletins. It increases by exactly
28008		* one second at the end of each positive UTC leap second,
28009		* introduced in order to keep UT1-UTC within +/- 0.9s. n.b. This
28010		* practice is under review, and in the future UT1-UTC may grow
28011		* essentially without limit.
28012		*
28013		* <li> The geographical coordinates are with respect to the WGS84
28014		* reference ellipsoid. TAKE CARE WITH THE LONGITUDE SIGN: the
28015		* longitude required by the present function is east-positive
28016		* (i.e. right-handed), in accordance with geographical convention.
28017		*
28018		* <li> The polar motion xp,yp can be obtained from IERS bulletins. The
28019		* values are the coordinates (in radians) of the Celestial
28020		* Intermediate Pole with respect to the International Terrestrial
28021		* Reference System (see IERS Conventions 2003), measured along the
28022		* meridians 0 and 90 deg west respectively. For many
28023		* applications, xp and yp can be set to zero.
28024		*
28025		* <li> If hm, the height above the ellipsoid of the observing station
28026		* in meters, is not known but phpa, the pressure in hPa (=mB), is
28027		* available, an adequate estimate of hm can be obtained from the
28028		* expression
28029		*
28030		* <p>hm = -29.3 * tsl * log ( phpa / 1013.25 );
28031		*
28032		* <p>where tsl is the approximate sea-level air temperature in K
28033		* (See Astrophysical Quantities, C.W.Allen, 3rd edition, section
28034		* 52). Similarly, if the pressure phpa is not known, it can be
28035		* estimated from the height of the observing station, hm, as
28036		* follows:
28037		*
28038		* <p>phpa = 1013.25 * exp ( -hm / ( 29.3 * tsl ) );
28039		*
28040		* <p>Note, however, that the refraction is nearly proportional to
28041		* the pressure and that an accurate phpa value is important for
28042		* precise work.
28043		*
28044		* <li> The argument wl specifies the observing wavelength in
28045		* micrometers. The transition from optical to radio is assumed to
28046		* occur at 100 micrometers (about 3000 GHz).
28047		*
28048		* <li> The accuracy of the result is limited by the corrections for
28049		* refraction, which use a simple Atan(z) + Btan^3(z) model.
28050		* Providing the meteorological parameters are known accurately and
28051		* there are no gross local effects, the predicted astrometric
28052		* coordinates should be within 0.05 arcsec (optical) or 1 arcsec
28053		* (radio) for a zenith distance of less than 70 degrees, better
28054		* than 30 arcsec (optical or radio) at 85 degrees and better
28055		* than 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
28056		*
28057		* <p>Without refraction, the complementary functions iauAtio13 and
28058		* iauAtoi13 are self-consistent to better than 1 microarcsecond
28059		* all over the celestial sphere. With refraction included,
28060		* consistency falls off at high zenith distances, but is still
28061		* better than 0.05 arcsec at 85 degrees.
28062		*
28063		* <li> It is advisable to take great care with units, as even unlikely
28064		* values of the input parameters are accepted and processed in
28065		* accordance with the models used.
28066		*
28067		* </ol>
28068		* Called:
28069		* <ul>
28070		* <li>{@link #jauApio13} astrometry parameters, CIRS-observed, 2013
28071		* <li>{@link #jauAtoiq} quick observed to CIRS
28072		*
28073		* </ul>
28074		*@version 2013 October 9
28075		*
28076		*@since JSOFA release 20131202
28077		*
28078		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28079		* @throws JSOFAInternalError
28080		* @throws JSOFAIllegalParameter
28081		*/
28082		public static SphericalCoordinate jauAtoi13(String type, double ob1, double ob2,
28083		double utc1, double utc2, double dut1,
28084		double elong, double phi, double hm, double xp, double yp,
28085		double phpa, double tc, double rh, double wl
28086		) throws JSOFAIllegalParameter, JSOFAInternalError
28087		{
28088	6	Astrom astrom = new Astrom();
28089
28090
28091		/* Star-independent astrometry parameters for CIRS->observed. */
28092	6	jauApio13(utc1, utc2, dut1, elong, phi, hm, xp, yp,
28093		phpa, tc, rh, wl, astrom);
28094
28095		/* Transform observed to CIRS. */
28096	6	SphericalCoordinate co = jauAtoiq(type, ob1, ob2, astrom);
28097	6	return co;
28098
28099		/* Finished. */
28100
28101
28102		}
28103
28104		/**
28105		* Quick observed place to CIRS, given the star-independent astrometry
28106		* parameters.
28107		*
28108		* Use of this function is appropriate when efficiency is important and
28109		* where many star positions are all to be transformed for one date.
28110		* The star-independent astrometry parameters can be obtained by
28111		* calling iauApio[13] or iauApco[13].
28112		*
28113		*<p>Status: support function.
28114		*
28115		*<!-- Given: -->
28116		* @param type char[] type of coordinates: "R", "H" or "A" (Note 1)
28117		* @param ob1 double observed Az, HA or RA (radians; Az is N=0,E=90)
28118		* @param ob2 double observed ZD or Dec (radians)
28119		* @param astrom star-independent astrometry parameters:
28120		*
28121		*<!-- Returned:-->
28122		* @return ri double* <b>Returned</b> CIRS right ascension (CIO-based, radians)
28123		* di double* <b>Returned</b> CIRS declination (radians)
28124		*
28125		*<p>Notes:
28126		* <ol>
28127		*
28128		* <li> "Observed" Az,El means the position that would be seen by a
28129		* perfect geodetically aligned theodolite. This is related to
28130		* the observed HA,Dec via the standard rotation, using the geodetic
28131		* latitude (corrected for polar motion), while the observed HA and
28132		* RA are related simply through the Earth rotation angle and the
28133		* site longitude. "Observed" RA,Dec or HA,Dec thus means the
28134		* position that would be seen by a perfect equatorial with its
28135		* polar axis aligned to the Earth's axis of rotation. By removing
28136		* from the observed place the effects of atmospheric refraction and
28137		* diurnal aberration, the CIRS RA,Dec is obtained.
28138		*
28139		* <li> Only the first character of the type argument is significant.
28140		* "R" or "r" indicates that ob1 and ob2 are the observed right
28141		* ascension and declination; "H" or "h" indicates that they are
28142		* hour angle (west +ve) and declination; anything else ("A" or
28143		* "a" is recommended) indicates that ob1 and ob2 are azimuth (north
28144		* zero, east 90 deg) and zenith distance. (Zenith distance is used
28145		* rather than altitude in order to reflect the fact that no
28146		* allowance is made for depression of the horizon.)
28147		*
28148		* <li> The accuracy of the result is limited by the corrections for
28149		* refraction, which use a simple Atan(z) + Btan^3(z) model.
28150		* Providing the meteorological parameters are known accurately and
28151		* there are no gross local effects, the predicted observed
28152		* coordinates should be within 0.05 arcsec (optical) or 1 arcsec
28153		* (radio) for a zenith distance of less than 70 degrees, better
28154		* than 30 arcsec (optical or radio) at 85 degrees and better than
28155		* 20 arcmin (optical) or 30 arcmin (radio) at the horizon.
28156		*
28157		* <p>Without refraction, the complementary functions iauAtioq and
28158		* iauAtoiq are self-consistent to better than 1 microarcsecond all
28159		* over the celestial sphere. With refraction included, consistency
28160		* falls off at high zenith distances, but is still better than
28161		* 0.05 arcsec at 85 degrees.
28162		*
28163		* <li> It is advisable to take great care with units, as even unlikely
28164		* values of the input parameters are accepted and processed in
28165		* accordance with the models used.
28166		*
28167		* </ol>
28168		* Called:
28169		* <ul>
28170		* <li>{@link #jauS2c} spherical coordinates to unit vector
28171		* <li>{@link #jauC2s} p-vector to spherical
28172		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
28173		*
28174		* </ul>
28175		*@version 2013 October 9
28176		*
28177		*@since JSOFA release 20131202
28178		*
28179		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28180		*/
28181		public static SphericalCoordinate jauAtoiq(String type,
28182		double ob1, double ob2, Astrom astrom
28183		)
28184		{
28185		char c;
28186	18	double c1, c2, sphi, cphi, ce, xaeo, yaeo, zaeo, v[] = new double[3],
28187		xmhdo, ymhdo, zmhdo, az, sz, zdo, refa, refb, tz, dref,
28188		zdt, xaet, yaet, zaet, xmhda, ymhda, zmhda,
28189		f, xhd, yhd, zhd, xpl, ypl, w;
28190
28191
28192		/* Coordinate type. */
28193	18	c = type.charAt(0);
28194
28195		/* Coordinates. */
28196	18	c1 = ob1;
28197	18	c2 = ob2;
28198
28199		/* Sin, cos of latitude. */
28200	18	sphi = astrom.sphi;
28201	18	cphi = astrom.cphi;
28202
28203		/* Standardize coordinate type. */
28204	18	if ( c == 'r' \|\| c == 'R' ) {
28205	6	c = 'R';
28206	12	} else if ( c == 'h' \|\| c == 'H' ) {
28207	6	c = 'H';
28208		} else {
28209	6	c = 'A';
28210		}
28211
28212		/* If Az,ZD, convert to Cartesian (S=0,E=90). */
28213	18	if ( c == 'A' ) {
28214	6	ce = sin(c2);
28215	6	xaeo = - cos(c1) * ce;
28216	6	yaeo = sin(c1) * ce;
28217	6	zaeo = cos(c2);
28218
28219		} else {
28220
28221		/* If RA,Dec, convert to HA,Dec. */
28222	12	if ( c == 'R' ) c1 = astrom.eral - c1;
28223
28224		/* To Cartesian -HA,Dec. */
28225	12	v = jauS2c ( -c1, c2 );
28226	12	xmhdo = v[0];
28227	12	ymhdo = v[1];
28228	12	zmhdo = v[2];
28229
28230		/* To Cartesian Az,El (S=0,E=90). */
28231	12	xaeo = sphixmhdo - cphizmhdo;
28232	12	yaeo = ymhdo;
28233	12	zaeo = cphixmhdo + sphizmhdo;
28234		}
28235
28236		/* Azimuth (S=0,E=90). */
28237	18	az = ( xaeo != 0.0 \|\| yaeo != 0.0 ) ? atan2(yaeo,xaeo) : 0.0;
28238
28239		/* Sine of observed ZD, and observed ZD. */
28240	18	sz = sqrt ( xaeoxaeo + yaeoyaeo );
28241	18	zdo = atan2 ( sz, zaeo );
28242
28243		/*
28244		* Refraction
28245		* ----------
28246		*/
28247
28248		/* Fast algorithm using two constant model. */
28249	18	refa = astrom.refa;
28250	18	refb = astrom.refb;
28251	18	tz = sz / zaeo;
28252	18	dref = ( refa + refbtztz ) * tz;
28253	18	zdt = zdo + dref;
28254
28255		/* To Cartesian Az,ZD. */
28256	18	ce = sin(zdt);
28257	18	xaet = cos(az) * ce;
28258	18	yaet = sin(az) * ce;
28259	18	zaet = cos(zdt);
28260
28261		/* Cartesian Az,ZD to Cartesian -HA,Dec. */
28262	18	xmhda = sphixaet + cphizaet;
28263	18	ymhda = yaet;
28264	18	zmhda = - cphixaet + sphizaet;
28265
28266		/* Diurnal aberration. */
28267	18	f = ( 1.0 + astrom.diurab*ymhda );
28268	18	xhd = f * xmhda;
28269	18	yhd = f * ( ymhda - astrom.diurab );
28270	18	zhd = f * zmhda;
28271
28272		/* Polar motion. */
28273	18	xpl = astrom.xpl;
28274	18	ypl = astrom.ypl;
28275	18	w = xplxhd - yplyhd + zhd;
28276	18	v[0] = xhd - xpl*w;
28277	18	v[1] = yhd + ypl*w;
28278	18	v[2] = w - ( xplxpl + yplypl ) * zhd;
28279
28280		/* To spherical -HA,Dec. */
28281	18	SphericalCoordinate co = jauC2s(v);
28282
28283		/* Right ascension. */
28284	18	co.alpha = jauAnp(astrom.eral + co.alpha);
28285
28286	18	return co;
28287		/* Finished. */
28288
28289
28290		}
28291
28292		/**
28293		* Apply light deflection by a solar-system body, as part of
28294		* transforming coordinate direction into natural direction.
28295		*
28296		*<p>This function is derived from the International Astronomical Union's
28297		* SOFA (Standards of Fundamental Astronomy) software collection.
28298		*
28299		*<p>Status: support function.
28300		*
28301		*<!-- Given: -->
28302		* @param bm double mass of the gravitating body (solar masses)
28303		* @param p double[3] direction from observer to source (unit vector)
28304		* @param q double[3] direction from body to source (unit vector)
28305		* @param e double[3] direction from body to observer (unit vector)
28306		* @param em double distance from body to observer (au)
28307		* @param dlim double deflection limiter (Note 4)
28308		*
28309		*<!-- Returned:-->
28310		* @return p1 double[3] <b>Returned</b> observer to deflected source (unit vector)
28311		*
28312		*<p>Notes:
28313		* <ol>
28314		*
28315		* <li> The algorithm is based on Expr. (70) in Klioner (2003) and
28316		* Expr. (7.63) in the Explanatory Supplement (Urban & Seidelmann
28317		* 2013), with some rearrangement to minimize the effects of machine
28318		* precision.
28319		*
28320		* <li> The mass parameter bm can, as required, be adjusted in order to
28321		* allow for such effects as quadrupole field.
28322		*
28323		* <li> The barycentric position of the deflecting body should ideally
28324		* correspond to the time of closest approach of the light ray to
28325		* the body.
28326		*
28327		* <li> The deflection limiter parameter dlim is phi^2/2, where phi is
28328		* the angular separation (in radians) between source and body at
28329		* which limiting is applied. As phi shrinks below the chosen
28330		* threshold, the deflection is artificially reduced, reaching zero
28331		* for phi = 0.
28332		*
28333		* <li> The returned vector p1 is not normalized, but the consequential
28334		* departure from unit magnitude is always negligible.
28335		*
28336		* <li> The arguments p and p1 can be the same array.
28337		*
28338		* <li> To accumulate total light deflection taking into account the
28339		* contributions from several bodies, call the present function for
28340		* each body in succession, in decreasing order of distance from the
28341		* observer.
28342		*
28343		* <li> For efficiency, validation is omitted. The supplied vectors must
28344		* be of unit magnitude, and the deflection limiter non-zero and
28345		* positive.
28346		*
28347		* </ol>
28348		*<p>References:
28349		* <ul>
28350		*
28351		* <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28352		* the Astronomical Almanac, 3rd ed., University Science Books
28353		* (2013).
28354		*
28355		* <li> Klioner, Sergei A., "A practical relativistic model for micro-
28356		* arcsecond astrometry in space", Astr. J. 125, 1580-1597 (2003).
28357		*
28358		* </ul>
28359		* Called:
28360		* <ul>
28361		* <li>{@link #jauPdp} scalar product of two p-vectors
28362		* <li>{@link #jauPxp} vector product of two p-vectors
28363		*
28364		* </ul>
28365		*@version 2013 October 9
28366		*
28367		*@since JSOFA release 20131202
28368		*
28369		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28370		*/
28371		public static double[] jauLd(double bm, double p[], double q[], double e[],
28372		double em, double dlim)
28373		{
28374		int i;
28375	104	double qpe[] = new double[3], qdqpe, w, eq[], peq[] ;
28376
28377	104	double p1[] = new double[3];
28378
28379		/* q . (q + e). */
28380	416	for (i = 0; i < 3; i++) {
28381	312	qpe[i] = q[i] + e[i];
28382		}
28383	104	qdqpe = jauPdp(q, qpe);
28384
28385		/* 2 x G x bm / ( em x c^2 x ( q . (q + e) ) ). */
28386	104	w = bm * SRS / em / max(qdqpe,dlim);
28387
28388		/* p x (e x q). */
28389	104	eq = jauPxp(e, q);
28390	104	peq = jauPxp(p, eq);
28391
28392		/* Apply the deflection. */
28393	416	for (i = 0; i < 3; i++) {
28394	312	p1[i] = p[i] + w*peq[i];
28395		}
28396
28397	104	return p1;
28398		/* Finished. */
28399
28400
28401		}
28402
28403		/*+
28404		* - - - - - - -
28405		* i a u L d n
28406		* - - - - - - -
28407		*
28408		* For a star, apply light deflection by multiple solar-system bodies,
28409		* as part of transforming coordinate direction into natural direction.
28410		*
28411		*<p>This function is derived from the International Astronomical Union's
28412		* SOFA (Standards of Fundamental Astronomy) software collection.
28413		*
28414		*<p>Status: support function.
28415		*
28416		*<!-- Given: -->
28417		* n int number of bodies (note 1)
28418		* b jauLDBODY[n] data for each of the n bodies (Notes 1,2):
28419		* bm double mass of the body (solar masses, Note 3)
28420		* dl double deflection limiter (Note 4)
28421		* pv [2][3] barycentric PV of the body (au, au/day)
28422		* ob double[3] barycentric position of the observer (au)
28423		* sc double[3] observer to star coord direction (unit vector)
28424		*
28425		*<!-- Returned:-->
28426		* sn double[3] observer to deflected star (unit vector)
28427		*
28428		* <li> The array b contains n entries, one for each body to be
28429		* considered. If n = 0, no gravitational light deflection will be
28430		* applied, not even for the Sun.
28431		*
28432		* <li> The array b should include an entry for the Sun as well as for
28433		* any planet or other body to be taken into account. The entries
28434		* should be in the order in which the light passes the body.
28435		*
28436		* <li> In the entry in the b array for body i, the mass parameter
28437		* b[i].bm can, as required, be adjusted in order to allow for such
28438		* effects as quadrupole field.
28439		*
28440		* <li> The deflection limiter parameter b[i].dl is phi^2/2, where phi is
28441		* the angular separation (in radians) between star and body at
28442		* which limiting is applied. As phi shrinks below the chosen
28443		* threshold, the deflection is artificially reduced, reaching zero
28444		* for phi = 0. Example values suitable for a terrestrial
28445		* observer, together with masses, are as follows:
28446		*
28447		* body i b[i].bm b[i].dl
28448		*
28449		* Sun 1.0 6e-6
28450		* Jupiter 0.00095435 3e-9
28451		* Saturn 0.00028574 3e-10
28452		*
28453		* <li> For cases where the starlight passes the body before reaching the
28454		* observer, the body is placed back along its barycentric track by
28455		* the light time from that point to the observer. For cases where
28456		* the body is "behind" the observer no such shift is applied. If
28457		* a different treatment is preferred, the user has the option of
28458		* instead using the iauLd function. Similarly, iauLd can be used
28459		* for cases where the source is nearby, not a star.
28460		*
28461		* <li> The returned vector sn is not normalized, but the consequential
28462		* departure from unit magnitude is always negligible.
28463		*
28464		* <li> The arguments sc and sn can be the same array.
28465		*
28466		* <li> For efficiency, validation is omitted. The supplied masses must
28467		* be greater than zero, the position and velocity vectors must be
28468		* right, and the deflection limiter greater than zero.
28469		*
28470		* Reference:
28471		*
28472		* Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28473		* the Astronomical Almanac, 3rd ed., University Science Books
28474		* (2013), Section 7.2.4.
28475		*
28476		* Called:
28477		* iauCp copy p-vector
28478		* iauPdp scalar product of two p-vectors
28479		* iauPmp p-vector minus p-vector
28480		* iauPpsp p-vector plus scaled p-vector
28481		* iauPn decompose p-vector into modulus and direction
28482		* iauLd light deflection by a solar-system body
28483		*
28484		*@version 2013 October 9
28485		*
28486		*@since JSOFA release 20131202
28487		*
28488		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28489		*/
28490		public static double[] jauLdn(int n, Ldbody b[], double ob[], double sc[])
28491		{
28492		/* Light time for 1 AU (days) */
28493	14	final double CR = AULT/DAYSEC;
28494
28495		int i;
28496	14	double v[] , dt, ev[], sn[] = new double[3];
28497
28498
28499		/* Star direction prior to deflection. */
28500	14	jauCp(sc, sn);
28501
28502		/* Body by body. */
28503	56	for ( i = 0; i < n; i++ ) {
28504
28505		/* Body to observer vector at epoch of observation (au). */
28506	42	v = jauPmp( ob, b[i].pv[0]);
28507
28508		/* Minus the time since the light passed the body (days). */
28509	42	dt = jauPdp(sn,v) * CR;
28510
28511		/* Neutralize if the star is "behind" the observer. */
28512	42	dt = min(dt, 0.0);
28513
28514		/* Backtrack the body to the time the light was passing the body. */
28515	42	ev = jauPpsp(v, -dt, b[i].pv[1]);
28516
28517		/* Body to observer vector as magnitude and direction. */
28518	42	NormalizedVector nv = jauPn(ev);
28519
28520		/* Apply light deflection for this body. */
28521	42	sn = jauLd( b[i].bm, sn, sn, nv.u, nv.r, b[i].dl );
28522
28523		/* Next body. */
28524		}
28525	14	return sn;
28526
28527		/* Finished. */
28528
28529
28530		}
28531
28532		/**
28533		* Deflection of starlight by the Sun.
28534		*
28535		*<p>This function is derived from the International Astronomical Union's
28536		* SOFA (Standards of Fundamental Astronomy) software collection.
28537		*
28538		*<p>Status: support function.
28539		*
28540		*<!-- Given: -->
28541		* @param p double[3] direction from observer to star (unit vector)
28542		* @param e double[3] direction from Sun to observer (unit vector)
28543		* @param em double distance from Sun to observer (au)
28544		*
28545		*<!-- Returned:-->
28546		* @return p1 double[3] <b>Returned</b> observer to deflected start (unit vector)
28547		*
28548		*<p>Notes:
28549		* <ol>
28550		*
28551		* <li> The source is presumed to be sufficiently distant that its
28552		* directions seen from the Sun and the observer are essentially
28553		* the same.
28554		*
28555		* <li> The deflection is restrained when the angle between the star and
28556		* the center of the Sun is less than a threshold value, falling to
28557		* zero deflection for zero separation. The chosen threshold value
28558		* is within the solar limb for all solar-system applications, and
28559		* is about 5 arcminutes for the case of a terrestrial observer.
28560		*
28561		* <li> The arguments p and p1 can be the same array.
28562		*
28563		* </ol>
28564		* Called:
28565		* <ul>
28566		* <li>{@link #jauLd} light deflection by a solar-system body
28567		*
28568		* </ul>
28569		*@version 2016 July 29
28570		*
28571		*@since JSOFA release 20131202
28572		*
28573		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28574		*/
28575		public static double[] jauLdsun(double p[], double e[], double em)
28576		{
28577		double em2, dlim;
28578
28579
28580		/* Deflection limiter (smaller for distant observers). */
28581	60	em2 = em*em;
28582	60	if ( em2 < 1.0 ) em2 = 1.0;
28583	60	dlim = 1e-6 / (em2 > 1.0 ? em2 : 1.0);
28584
28585		/* Apply the deflection. */
28586	60	return jauLd(1.0, p, p, e, em, dlim);
28587
28588		}
28589
28590		/**
28591		* Proper motion and parallax.
28592		*
28593		*<p>This function is derived from the International Astronomical Union's
28594		* SOFA (Standards of Fundamental Astronomy) software collection.
28595		*
28596		*<p>Status: support function.
28597		*
28598		*<!-- Given: -->
28599		* @param rc double ICRS RA,Dec at catalog epoch (radians)
28600		* @param dc double ICRS RA,Dec at catalog epoch (radians)
28601		* @param pr double RA proper motion (radians/year; Note 1)
28602		* @param pd double Dec proper motion (radians/year)
28603		* @param px double parallax (arcsec)
28604		* @param rv double radial velocity (km/s, +ve if receding)
28605		* @param pmt double proper motion time interval (SSB, Julian years)
28606		* @param pob double[3] SSB to observer vector (au)
28607		*
28608		*<!-- Returned:-->
28609		* @return pco double[3] <b>Returned</b> coordinate direction (BCRS unit vector)
28610		*
28611		*<p>Notes:
28612		* <ol>
28613		*
28614		* <li> The proper motion in RA is dRA/dt rather than cos(Dec)*dRA/dt.
28615		*
28616		* <li> The proper motion time interval is for when the starlight
28617		* reaches the solar system barycenter.
28618		*
28619		* <li> To avoid the need for iteration, the Roemer effect (i.e. the
28620		* small annual modulation of the proper motion coming from the
28621		* changing light time) is applied approximately, using the
28622		* direction of the star at the catalog epoch.
28623		*
28624		* </ol>
28625		*<p>References:
28626		* <ul>
28627		*
28628		* <li> 1984 Astronomical Almanac, pp B39-B41.
28629		*
28630		* <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28631		* the Astronomical Almanac, 3rd ed., University Science Books
28632		* (2013), Section 7.2.
28633		*
28634		* </ul>
28635		* Called:
28636		* <ul>
28637		* <li>{@link #jauPdp} scalar product of two p-vectors
28638		* <li>{@link #jauPn} decompose p-vector into modulus and direction
28639		*
28640		* </ul>
28641		*@version 2013 October 9
28642		*
28643		*@since JSOFA release 20131202
28644		*
28645		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28646		*/
28647		public static double[] jauPmpx(double rc, double dc, double pr, double pd,
28648		double px, double rv, double pmt, double pob[]
28649		)
28650		{
28651		/* Km/s to au/year */
28652	10	final double VF = DAYSEC*DJM/DAU;
28653
28654		/* Light time for 1 au, Julian years */
28655	10	final double AULTY = AULT/DAYSEC/DJY;
28656
28657		int i;
28658	10	double sr, cr, sd, cd, x, y, z, p[] = new double[3], dt, pxr, w, pdz, pm[] = new double[3];
28659
28660
28661		/* Spherical coordinates to unit vector (and useful functions). */
28662	10	sr = sin(rc);
28663	10	cr = cos(rc);
28664	10	sd = sin(dc);
28665	10	cd = cos(dc);
28666	10	p[0] = x = cr*cd;
28667	10	p[1] = y = sr*cd;
28668	10	p[2] = z = sd;
28669
28670		/* Proper motion time interval (y) including Roemer effect. */
28671	10	dt = pmt + jauPdp(p,pob)*AULTY;
28672
28673		/* Space motion (radians per year). */
28674	10	pxr = px * DAS2R;
28675	10	w = VF * rv * pxr;
28676	10	pdz = pd * z;
28677	10	pm[0] = - pry - pdzcr + w*x;
28678	10	pm[1] = prx - pdzsr + w*y;
28679	10	pm[2] = pdcd + wz;
28680
28681		/* Coordinate direction of star (unit vector, BCRS). */
28682	40	for (i = 0; i < 3; i++) {
28683	30	p[i] += dtpm[i] - pxrpob[i];
28684		}
28685	10	NormalizedVector pco = jauPn(p);
28686
28687	10	return pco.u;
28688		/* Finished. */
28689
28690
28691		}
28692
28693		/**
28694		* Star proper motion: update star catalog data for space motion, with
28695		* special handling to handle the zero parallax case.
28696		*
28697		*<p>This function is derived from the International Astronomical Union's
28698		* SOFA (Standards of Fundamental Astronomy) software collection.
28699		*
28700		*<p>Status: support function.
28701		*
28702		*<!-- Given: -->
28703		* @param ra1 double right ascension (radians), before
28704		* @param dec1 double declination (radians), before
28705		* @param pmr1 double RA proper motion (radians/year), before
28706		* @param pmd1 double Dec proper motion (radians/year), before
28707		* @param px1 double parallax (arcseconds), before
28708		* @param rv1 double radial velocity (km/s, +ve = receding), before
28709		* @param ep1a double "before" epoch, part A (Note 1)
28710		* @param ep1b double "before" epoch, part B (Note 1)
28711		* @param ep2a double "after" epoch, part A (Note 1)
28712		* @param ep2b double "after" epoch, part B (Note 1)
28713		*
28714		*<!-- Returned:-->
28715		* @return ra2 double <b>Returned</b> right ascension (radians), after
28716		* dec2 double <b>Returned</b> declination (radians), after
28717		* pmr2 double <b>Returned</b> RA proper motion (radians/year), after
28718		* pmd2 double <b>Returned</b> Dec proper motion (radians/year), after
28719		* px2 double <b>Returned</b> parallax (arcseconds), after
28720		* rv2 double <b>Returned</b> radial velocity (km/s, +ve = receding), after
28721		*
28722		* @throws JSOFAInternalError
28723		* int status:
28724		* -1 = <b>Returned</b> system error (should not occur)
28725		* 0 = <b>Returned</b> no warnings or errors
28726		* 1 = <b>Returned</b> distance overridden (Note 6)
28727		* 2 = <b>Returned</b> excessive velocity (Note 7)
28728		* 4 = <b>Returned</b> solution didn't converge (Note 8)
28729		* else = <b>Returned</b> binary logical OR of the above warnings
28730		*
28731		*<p>Notes:
28732		* <ol>
28733		*
28734		* <li> The starting and ending TDB epochs ep1a+ep1b and ep2a+ep2b are
28735		* Julian Dates, apportioned in any convenient way between the two
28736		* parts (A and B). For example, JD(TDB)=2450123.7 could be
28737		* expressed in any of these ways, among others:
28738		*
28739		* <p>epNa epNb
28740		*
28741		* 2450123.7 0.0 (JD method)
28742		* 2451545.0 -1421.3 (J2000 method)
28743		* 2400000.5 50123.2 (MJD method)
28744		* 2450123.5 0.2 (date & time method)
28745		*
28746		* <p>The JD method is the most natural and convenient to use in cases
28747		* where the loss of several decimal digits of resolution is
28748		* acceptable. The J2000 method is best matched to the way the
28749		* argument is handled internally and will deliver the optimum
28750		* resolution. The MJD method and the date & time methods are both
28751		* good compromises between resolution and convenience.
28752		*
28753		* <li> In accordance with normal star-catalog conventions, the object's
28754		* right ascension and declination are freed from the effects of
28755		* secular aberration. The frame, which is aligned to the catalog
28756		* equator and equinox, is Lorentzian and centered on the SSB.
28757		*
28758		* <p>The proper motions are the rate of change of the right ascension
28759		* and declination at the catalog epoch and are in radians per TDB
28760		* Julian year.
28761		*
28762		* <p>The parallax and radial velocity are in the same frame.
28763		*
28764		* <li> Care is needed with units. The star coordinates are in radians
28765		* and the proper motions in radians per Julian year, but the
28766		* parallax is in arcseconds.
28767		*
28768		* <li> The RA proper motion is in terms of coordinate angle, not true
28769		* angle. If the catalog uses arcseconds for both RA and Dec proper
28770		* motions, the RA proper motion will need to be divided by cos(Dec)
28771		* before use.
28772		*
28773		* <li> Straight-line motion at constant speed, in the inertial frame, is
28774		* assumed.
28775		*
28776		* <li> An extremely small (or zero or negative) parallax is overridden
28777		* to ensure that the object is at a finite but very large distance,
28778		* but not so large that the proper motion is equivalent to a large
28779		* but safe speed (about 0.1c using the chosen constant). A warning
28780		* status of 1 is added to the status if this action has been taken.
28781		*
28782		* <li> If the space velocity is a significant fraction of c (see the
28783		* constant VMAX in the function iauStarpv), it is arbitrarily set
28784		* to zero. When this action occurs, 2 is added to the status.
28785		*
28786		* <li> The relativistic adjustment carried out in the iauStarpv function
28787		* involves an iterative calculation. If the process fails to
28788		* converge within a set number of iterations, 4 is added to the
28789		* status.
28790		*
28791		* </ol>
28792		* Called:
28793		* <ul>
28794		* <li>{@link #jauSeps} angle between two points
28795		* <li>{@link #jauStarpm} update star catalog data for space motion
28796		*
28797		* </ul>
28798		*@version 2013 October 9
28799		*
28800		*@since JSOFA release 20131202
28801		*
28802		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28803		* @throws JSOFAInternalError
28804		*/
28805		public static CatalogCoords jauPmsafe(double ra1, double dec1, double pmr1, double pmd1,
28806		double px1, double rv1,
28807		double ep1a, double ep1b, double ep2a, double ep2b) throws JSOFAInternalError
28808		{
28809
28810		/* Minimum allowed parallax (arcsec) */
28811	2	final double PXMIN = 5e-7;
28812
28813		/* Factor giving maximum allowed transverse speed of about 1% c */
28814	2	final double F = 326.0;
28815
28816		double pm, px1a;
28817
28818
28819		/* Proper motion in one year (radians). */
28820	2	pm = jauSeps(ra1, dec1, ra1+pmr1, dec1+pmd1);
28821
28822
28823	2	px1a = px1;
28824	2	pm *= F;
28825	2	if (px1a < pm) {px1a = pm;}
28826	2	if (px1a < PXMIN) {px1a = PXMIN;}
28827
28828		/* Carry out the transformation using the modified parallax. */
28829	2	return jauStarpm(ra1, dec1, pmr1, pmd1, px1a, rv1,
28830		ep1a, ep1b, ep2a, ep2b);
28831
28832		/* Finished. */
28833
28834
28835		}
28836
28837		/**
28838		* Position and velocity of a terrestrial observing station.
28839		*
28840		*<p>This function is derived from the International Astronomical Union's
28841		* SOFA (Standards of Fundamental Astronomy) software collection.
28842		*
28843		*<p>Status: support function.
28844		*
28845		*<!-- Given: -->
28846		* @param elong double longitude (radians, east +ve, Note 1)
28847		* @param phi double latitude (geodetic, radians, Note 1)
28848		* @param hm double height above ref. ellipsoid (geodetic, m)
28849		* @param xp double coordinates of the pole (radians, Note 2)
28850		* @param yp double coordinates of the pole (radians, Note 2)
28851		* @param sp double the TIO locator s' (radians, Note 2)
28852		* @param theta double Earth rotation angle (radians, Note 3)
28853		*
28854		*<!-- Returned:-->
28855		* @return pv double[2][3] <b>Returned</b> position/velocity vector (m, m/s, CIRS)
28856		*
28857		*<p>Notes:
28858		* <ol>
28859		*
28860		* <li> The terrestrial coordinates are with respect to the WGS84
28861		* reference ellipsoid.
28862		*
28863		* <li> xp and yp are the coordinates (in radians) of the Celestial
28864		* Intermediate Pole with respect to the International Terrestrial
28865		* Reference System (see IERS Conventions), measured along the
28866		* meridians 0 and 90 deg west respectively. sp is the TIO locator
28867		* s', in radians, which positions the Terrestrial Intermediate
28868		* Origin on the equator. For many applications, xp, yp and
28869		* (especially) sp can be set to zero.
28870		*
28871		* <li> If theta is Greenwich apparent sidereal time instead of Earth
28872		* rotation angle, the result is with respect to the true equator
28873		* and equinox of date, i.e. with the x-axis at the equinox rather
28874		* than the celestial intermediate origin.
28875		*
28876		* <li> The velocity units are meters per UT1 second, not per SI second.
28877		* This is unlikely to have any practical consequences in the modern
28878		* era.
28879		*
28880		* <li> No validation is performed on the arguments. Error cases that
28881		* could lead to arithmetic exceptions are trapped by the iauGd2gc
28882		* function, and the result set to zeros.
28883		*
28884		* </ol>
28885		*<p>References:
28886		* <ul>
28887		*
28888		* <li> McCarthy, D. D., Petit, G. (eds.), IERS Conventions (2003),
28889		* IERS Technical Note No. 32, BKG (2004)
28890		*
28891		* <li> Urban, S. & Seidelmann, P. K. (eds), Explanatory Supplement to
28892		* the Astronomical Almanac, 3rd ed., University Science Books
28893		* (2013), Section 7.4.3.3.
28894		*
28895		* </ul>
28896		* Called:
28897		* <ul>
28898		* <li>{@link #jauGd2gc} geodetic to geocentric transformation
28899		* <li>{@link #jauPom00} polar motion matrix
28900		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
28901		*
28902		* </ul>
28903		*@version 2013 October 9
28904		*
28905		* @since JSOFA release 20131202
28906		*
28907		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
28908		* @throws JSOFAInternalError
28909		* @throws JSOFAIllegalParameter
28910		*/
28911		public static double [][] jauPvtob(double elong, double phi, double hm,
28912		double xp, double yp, double sp, double theta
28913		) throws JSOFAIllegalParameter, JSOFAInternalError
28914		{
28915
28916		double xyzm[];
28917
28918		/* Geodetic to geocentric transformation (WGS84). */
28919	30	xyzm = jauGd2gc(1, elong, phi, hm);
28920
28921	30	return jauPvtob(xyzm, xp, yp, sp, theta );
28922		/* Finished. */
28923
28924
28925		}
28926
28927		/**
28928		* Alternative Position and velocity of a terrestrial observing station with observatory position already in cartesian.
28929		* @see JSOFA#jauPvtob(double, double, double, double, double, double, double) for more detail.
28930		* @param xyzm observatory geocentric position in metres.
28931		* @param xp double coordinates of the pole (radians, Note 2)
28932		* @param yp double coordinates of the pole (radians, Note 2)
28933		* @param sp double the TIO locator s' (radians, Note 2)
28934		* @param theta double Earth rotation angle (radians, Note 3)
28935		* @return pv double[2][3] <b>Returned</b> position/velocity vector (m, m/s, CIRS)
28936		* @throws JSOFAIllegalParameter
28937		* @throws JSOFAInternalError
28938		*/
28939		public static double [][] jauPvtob(double xyzm[],
28940		double xp, double yp, double sp, double theta
28941		) throws JSOFAIllegalParameter, JSOFAInternalError
28942		{
28943		/* Earth rotation rate in radians per UT1 second */
28944	30	final double OM = 1.00273781191135448 * D2PI / DAYSEC;
28945
28946		double rpm[][], xyz[], x, y, z, s, c;
28947	30	double pv[][] = new double[2][3];
28948
28949
28950		/* Polar motion and TIO position. */
28951	30	rpm = jauPom00(xp, yp, sp);
28952	30	xyz = jauTrxp(rpm, xyzm);
28953	30	x = xyz[0];
28954	30	y = xyz[1];
28955	30	z = xyz[2];
28956
28957		/* Functions of ERA. */
28958	30	s = sin(theta);
28959	30	c = cos(theta);
28960
28961		/* Position. */
28962	30	pv[0][0] = cx - sy;
28963	30	pv[0][1] = sx + cy;
28964	30	pv[0][2] = z;
28965
28966		/* Velocity. */
28967	30	pv[1][0] = OM * ( -sx - cy );
28968	30	pv[1][1] = OM * ( cx - sy );
28969	30	pv[1][2] = 0.0;
28970
28971	30	return pv;
28972		/* Finished. */
28973
28974
28975		}
28976
28977		/**
28978		* constants A and B in the atmospheric refraction model
28979		* dZ = A tan Z + B tan^3 Z.
28980		* .
28981		* @author Paul Harrison (paul.harrison@manchester.ac.uk) 28 Mar 2014
28982		* @version $Revision$ $date$
28983		*/
28984		public static class RefCos {
28985		/** refraction coefficient A */
28986		public double a ;
28987
28988		/** refraction coefficient B */
28989		public double b ;
28990	26	public RefCos(double a, double b) {
28991	26	this.a = a;
28992	26	this.b = b;
28993	26	}
28994
28995		}
28996
28997		/**
28998		* Determine the constants A and B in the atmospheric refraction model
28999		* dZ = A tan Z + B tan^3 Z.
29000		*
29001		* Z is the "observed" zenith distance (i.e. affected by refraction)
29002		* and dZ is what to add to Z to give the "topocentric" (i.e. in vacuo)
29003		* zenith distance.
29004		*
29005		*<p>This function is derived from the International Astronomical Union's
29006		* SOFA (Standards of Fundamental Astronomy) software collection.
29007		*
29008		*<p>Status: support function.
29009		*
29010		*<!-- Given: -->
29011		* @param phpa double pressure at the observer (hPa = millibar)
29012		* @param tc double ambient temperature at the observer (deg C)
29013		* @param rh double relative humidity at the observer (range 0-1)
29014		* @param wl double wavelength (micrometers)
29015		*
29016		*<!-- Returned:-->
29017		* @return <b>Returned</b> tan Z coefficient (radians)
29018		* <b>Returned</b> tan^3 Z coefficient (radians)
29019		*
29020		*<p>Notes:
29021		* <ol>
29022		*
29023		* <li> The model balances speed and accuracy to give good results in
29024		* applications where performance at low altitudes is not paramount.
29025		* Performance is maintained across a range of conditions, and
29026		* applies to both optical/IR and radio.
29027		*
29028		* <li> The model omits the effects of (i) height above sea level (apart
29029		* from the reduced pressure itself), (ii) latitude (i.e. the
29030		* flattening of the Earth), (iii) variations in tropospheric lapse
29031		* rate and (iv) dispersive effects in the radio.
29032		*
29033		* <p>The model was tested using the following range of conditions:
29034		*
29035		* <p>lapse rates 0.0055, 0.0065, 0.0075 deg/meter
29036		* latitudes 0, 25, 50, 75 degrees
29037		* heights 0, 2500, 5000 meters ASL
29038		* pressures mean for height -10% to +5% in steps of 5%
29039		* temperatures -10 deg to +20 deg with respect to 280 deg at SL
29040		* relative humidity 0, 0.5, 1
29041		* wavelengths 0.4, 0.6, ... 2 micron, + radio
29042		* zenith distances 15, 45, 75 degrees
29043		*
29044		* <p>The accuracy with respect to raytracing through a model
29045		* atmosphere was as follows:
29046		*
29047		* <p>worst RMS
29048		*
29049		* <p>optical/IR 62 mas 8 mas
29050		* radio 319 mas 49 mas
29051		*
29052		* <p>For this particular set of conditions:
29053		*
29054		* <p>lapse rate 0.0065 K/meter
29055		* latitude 50 degrees
29056		* sea level
29057		* pressure 1005 mb
29058		* temperature 280.15 K
29059		* humidity 80%
29060		* wavelength 5740 Angstroms
29061		*
29062		* <p>the results were as follows:
29063		*
29064		* <p>ZD raytrace iauRefco Saastamoinen
29065		*
29066		* 10 10.27 10.27 10.27
29067		* 20 21.19 21.20 21.19
29068		* 30 33.61 33.61 33.60
29069		* 40 48.82 48.83 48.81
29070		* 45 58.16 58.18 58.16
29071		* 50 69.28 69.30 69.27
29072		* 55 82.97 82.99 82.95
29073		* 60 100.51 100.54 100.50
29074		* 65 124.23 124.26 124.20
29075		* 70 158.63 158.68 158.61
29076		* 72 177.32 177.37 177.31
29077		* 74 200.35 200.38 200.32
29078		* 76 229.45 229.43 229.42
29079		* 78 267.44 267.29 267.41
29080		* 80 319.13 318.55 319.10
29081		*
29082		* <p>deg arcsec arcsec arcsec
29083		*
29084		* <p>The values for Saastamoinen's formula (which includes terms
29085		* up to tan^5) are taken from Hohenkerk and Sinclair (1985).
29086		*
29087		* <li> A wl value in the range 0-100 selects the optical/IR case and is
29088		* wavelength in micrometers. Any value outside this range selects
29089		* the radio case.
29090		*
29091		* <li> Outlandish input parameters are silently limited to
29092		* mathematically safe values. Zero pressure is permissible, and
29093		* causes zeroes to be returned.
29094		*
29095		* <li> The algorithm draws on several sources, as follows:
29096		*
29097		* <p>a) The formula for the saturation vapour pressure of water as
29098		* a function of temperature and temperature is taken from
29099		* Equations (A4.5-A4.7) of Gill (1982).
29100		*
29101		* <p>b) The formula for the water vapour pressure, given the
29102		* saturation pressure and the relative humidity, is from
29103		* Crane (1976), Equation (2.5.5).
29104		*
29105		* <p>c) The refractivity of air is a function of temperature,
29106		* total pressure, water-vapour pressure and, in the case
29107		* of optical/IR, wavelength. The formulae for the two cases are
29108		* developed from Hohenkerk & Sinclair (1985) and Rueger (2002).
29109		*
29110		* <p>d) The formula for beta, the ratio of the scale height of the
29111		* atmosphere to the geocentric distance of the observer, is
29112		* an adaption of Equation (9) from Stone (1996). The
29113		* adaptations, arrived at empirically, consist of (i) a small
29114		* adjustment to the coefficient and (ii) a humidity term for the
29115		* radio case only.
29116		*
29117		* <p>e) The formulae for the refraction constants as a function of
29118		* n-1 and beta are from Green (1987), Equation (4.31).
29119		*
29120		* </ol>
29121		*<p>References:
29122		* <ul>
29123		*
29124		* <li> Crane, R.K., Meeks, M.L. (ed), "Refraction Effects in the Neutral
29125		* Atmosphere", Methods of Experimental Physics: Astrophysics 12B,
29126		* Academic Press, 1976.
29127		*
29128		* <li> Gill, Adrian E., "Atmosphere-Ocean Dynamics", Academic Press,
29129		* 1982.
29130		*
29131		* <li> Green, R.M., "Spherical Astronomy", Cambridge University Press,
29132		* 1987.
29133		*
29134		* <li> Hohenkerk, C.Y., & Sinclair, A.T., NAO Technical Note No. 63,
29135		* 1985.
29136		*
29137		* <li> Rueger, J.M., "Refractive Index Formulae for Electronic Distance
29138		* Measurement with Radio and Millimetre Waves", in Unisurv Report
29139		* S-68, School of Surveying and Spatial Information Systems,
29140		* University of New South Wales, Sydney, Australia, 2002.
29141		*
29142		* <li> Stone, Ronald C., P.A.S.P. 108, 1051-1058, 1996.
29143		*
29144		* </ul>
29145		*@version 2013 October 9
29146		*
29147		*@since JSOFA release 20131202
29148		*
29149		* <!-- Copyright (C) 2013 IAU SOFA Board. See notes at end. -->
29150		*/
29151		public static RefCos jauRefco(double phpa, double tc, double rh, double wl )
29152		{
29153		boolean optic;
29154		double p, t, r, w, ps, pw, tk, wlsq, gamma, beta;
29155
29156
29157		/* Decide whether optical/IR or radio case: switch at 100 microns. */
29158	26	optic = ( wl <= 100.0 );
29159
29160		/* Restrict parameters to safe values. */
29161	26	t = max ( tc, -150.0 );
29162	26	t = min ( t, 200.0 );
29163	26	p = max ( phpa, 0.0 );
29164	26	p = min ( p, 10000.0 );
29165	26	r = max ( rh, 0.0 );
29166	26	r = min ( r, 1.0 );
29167	26	w = max ( wl, 0.1 );
29168	26	w = min ( w, 1e6 );
29169
29170		/* Water vapour pressure at the observer. */
29171	26	if ( p > 0.0 ) {
29172	26	ps = pow ( 10.0, ( 0.7859 + 0.03477*t ) /
29173		( 1.0 + 0.00412t ) )
29174		( 1.0 + p * ( 4.5e-6 + 6e-10tt ) );
29175	26	pw = r * ps / ( 1.0 - (1.0-r)*ps/p );
29176		} else {
29177	0	pw = 0.0;
29178		}
29179
29180		/* Refractive index minus 1 at the observer. */
29181	26	tk = t + 273.15;
29182	26	if ( optic ) {
29183	26	wlsq = w * w;
29184	26	gamma = ( ( 77.53484e-6 +
29185		( 4.39108e-7 + 3.666e-9/wlsq ) / wlsq ) * p
29186		- 11.2684e-6*pw ) / tk;
29187		} else {
29188	0	gamma = ( 77.6890e-6p - ( 6.3938e-6 - 0.375463/tk ) pw ) / tk;
29189		}
29190
29191		/* Formula for beta from Stone, with empirical adjustments. */
29192	26	beta = 4.4474e-6 * tk;
29193	26	if ( ! optic ) beta -= 0.0074 * pw * beta;
29194
29195		/* Refraction constants from Green. */
29196	26	return new RefCos( gamma * ( 1.0 - beta ),
29197		- gamma * ( beta - gamma / 2.0 ));
29198
29199		/* Finished. */
29200
29201
29202		}
29203
29204
29205		/**
29206		* Transformation from Galactic Coordinates to ICRS.
29207		*
29208		* This function is derived from the International Astronomical Union's
29209		* SOFA (Standards of Fundamental Astronomy) software collection.
29210		*
29211		* <p>Status: support routine.
29212		*
29213		* @param dl double galactic longitude (radians)
29214		* @param db double galactic latitude (radians)
29215		*
29216		* @return co ICRS right ascension, declination.
29217		*
29218		* <p>Notes:<ol>
29219		*
29220		* <li> The IAU 1958 system of Galactic coordinates was defined with
29221		* respect to the now obsolete reference system FK4 B1950.0. When
29222		* interpreting the system in a modern context, several factors have
29223		* to be taken into account:<ul>
29224		*
29225		* <li> The inclusion in FK4 positions of the E-terms of aberration.
29226		*
29227		* <li> The distortion of the FK4 proper motion system by differential
29228		* Galactic rotation.
29229		*
29230		* <li> The use of the B1950.0 equinox rather than the now-standard
29231		* J2000.0.
29232		*
29233		* <li> The frame bias between ICRS and the J2000.0 mean place system.
29234		* </ul>
29235		* The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
29236		* matrix that transforms directly between ICRS and Galactic
29237		* coordinates with the above factors taken into account. The
29238		* matrix is derived from three angles, namely the ICRS coordinates
29239		* of the Galactic pole and the longitude of the ascending node of
29240		* the galactic equator on the ICRS equator. They are given in
29241		* degrees to five decimal places and for canonical purposes are
29242		* regarded as exact. In the Hipparcos Catalogue the matrix
29243		* elements are given to 10 decimal places (about 20 microarcsec).
29244		* In the present SOFA function the matrix elements have been
29245		* recomputed from the canonical three angles and are given to 30
29246		* decimal places.
29247		*
29248		* <li> The inverse transformation is performed by the function jauIcrs2g.
29249		* </ol>
29250		*
29251		* Reference:
29252		* Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
29253		* catalogues. Astrometric and photometric star catalogues
29254		* derived from the ESA Hipparcos Space Astrometry Mission. ESA
29255		* Publications Division, Noordwijk, Netherlands.
29256		*
29257		* @version 2015 March 02
29258		*
29259		*
29260		* @since JSOFA release 20150209
29261		*
29262		*/
29263		public static SphericalCoordinate jauG2icrs ( double dl, double db)
29264		{
29265		double v1[], v2[];
29266
29267		/*
29268		* L2,B2 system of galactic coordinates in the form presented in the
29269		* Hipparcos Catalogue. In degrees:
29270		*
29271		* P = 192.85948 right ascension of the Galactic north pole in ICRS
29272		* Q = 27.12825 declination of the Galactic north pole in ICRS
29273		* R = 32.93192 longitude of the ascending node of the Galactic
29274		* plane on the ICRS equator
29275		*
29276		* ICRS to galactic rotation matrix, obtained by computing
29277		* R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown:
29278		*/
29279	2	double r[][] = new double[][]{ { -0.054875560416215368492398900454,
29280		-0.873437090234885048760383168409,
29281		-0.483835015548713226831774175116 },
29282		{ +0.494109427875583673525222371358,
29283		-0.444829629960011178146614061616,
29284		+0.746982244497218890527388004556 },
29285		{ -0.867666149019004701181616534570,
29286		-0.198076373431201528180486091412,
29287		+0.455983776175066922272100478348 } };
29288
29289
29290		/* Spherical to Cartesian. */
29291	2	v1 = jauS2c(dl, db);
29292
29293		/* Galactic to ICRS. */
29294	2	v2 = jauTrxp(r, v1);
29295
29296		/* Cartesian to spherical. */
29297	2	SphericalCoordinate co = jauC2s(v2);
29298
29299		/* Express in conventional ranges. */
29300	2	co.alpha = jauAnp(co.alpha);
29301	2	co.delta = jauAnpm(co.delta);
29302
29303		/* Finished. */
29304	2	return co;
29305		}
29306
29307
29308
29309		/**
29310		* Transformation from ICRS to Galactic Coordinates.
29311		*
29312		* This function is derived from the International Astronomical Union's
29313		* SOFA (Standards of Fundamental Astronomy) software collection.
29314		*
29315		* <p>Status: support routine.
29316		*
29317		* @param dr double ICRS right ascension (radians)
29318		* @param dd double ICRS declination (radians)
29319		*
29320		* @return co galactic longitude (radians), galactic latitude (radians)
29321		*
29322		* <p>Notes:<ol>
29323		*
29324		* <li> The IAU 1958 system of Galactic coordinates was defined with
29325		* respect to the now obsolete reference system FK4 B1950.0. When
29326		* interpreting the system in a modern context, several factors have
29327		* to be taken into account:<ul>
29328		*
29329		* <li> The inclusion in FK4 positions of the E-terms of aberration.
29330		*
29331		* <li> The distortion of the FK4 proper motion system by differential
29332		* Galactic rotation.
29333		*
29334		* <li> The use of the B1950.0 equinox rather than the now-standard
29335		* J2000.0.
29336		*
29337		* <li> The frame bias between ICRS and the J2000.0 mean place system.
29338		* </ul>
29339		* The Hipparcos Catalogue (Perryman & ESA 1997) provides a rotation
29340		* matrix that transforms directly between ICRS and Galactic
29341		* coordinates with the above factors taken into account. The
29342		* matrix is derived from three angles, namely the ICRS coordinates
29343		* of the Galactic pole and the longitude of the ascending node of
29344		* the galactic equator on the ICRS equator. They are given in
29345		* degrees to five decimal places and for canonical purposes are
29346		* regarded as exact. In the Hipparcos Catalogue the matrix
29347		* elements are given to 10 decimal places (about 20 microarcsec).
29348		* In the present SOFA function the matrix elements have been
29349		* recomputed from the canonical three angles and are given to 30
29350		* decimal places.
29351		*
29352		* <li> The inverse transformation is performed by the function iauG2icrs.
29353		* </ol>
29354		* Reference:
29355		* Perryman M.A.C. & ESA, 1997, ESA SP-1200, The Hipparcos and Tycho
29356		* catalogues. Astrometric and photometric star catalogues
29357		* derived from the ESA Hipparcos Space Astrometry Mission. ESA
29358		* Publications Division, Noordwijk, Netherlands.
29359		*
29360		* @version 2015 January 20
29361		*
29362		* @since JSOFA release 20150209
29363		*
29364		*/
29365		public static SphericalCoordinate jauIcrs2g ( double dr, double dd )
29366		{
29367		double v1[], v2[];
29368
29369		/*
29370		* L2,B2 system of galactic coordinates in the form presented in the
29371		* Hipparcos Catalogue. In degrees:
29372		*
29373		* P = 192.85948 right ascension of the Galactic north pole in ICRS
29374		* Q = 27.12825 declination of the Galactic north pole in ICRS
29375		* R = 32.93192 longitude of the ascending node of the Galactic
29376		* plane on the ICRS equator
29377		*
29378		* ICRS to galactic rotation matrix, obtained by computing
29379		* R_3(-R) R_1(pi/2-Q) R_3(pi/2+P) to the full precision shown:
29380		*/
29381	2	double r[][] = new double[][] { { -0.054875560416215368492398900454,
29382		-0.873437090234885048760383168409,
29383		-0.483835015548713226831774175116 },
29384		{ +0.494109427875583673525222371358,
29385		-0.444829629960011178146614061616,
29386		+0.746982244497218890527388004556 },
29387		{ -0.867666149019004701181616534570,
29388		-0.198076373431201528180486091412,
29389		+0.455983776175066922272100478348 } };
29390
29391
29392		/* Spherical to Cartesian. */
29393	2	v1 = jauS2c(dr, dd);
29394
29395		/* ICRS to Galactic. */
29396	2	v2 = jauRxp(r, v1);
29397
29398		/* Cartesian to spherical. */
29399	2	SphericalCoordinate co = jauC2s(v2);
29400
29401		/* Express in conventional ranges. */
29402	2	co.alpha = jauAnp(co.alpha);
29403	2	co.delta = jauAnpm(co.delta);
29404	2	return co;
29405		}
29406
29407		// 2016-05-03 additions below
29408
29409		/**
29410		*
29411		* Transformation from ecliptic coordinates (mean equinox and ecliptic
29412		* of date) to ICRS RA,Dec, using the IAU 2006 precession model.
29413		*
29414		* <p>This function is derived from the International Astronomical Union's
29415		* SOFA (Standards of Fundamental Astronomy) software collection.
29416		*
29417		* <p>Status: support function.
29418		*
29419		* <!-- Given: -->
29420		* @param date1 double TT as a 2-part Julian date (Note 1)
29421		* @param date2 double TT as a 2-part Julian date (Note 1)
29422		* @param dl double ecliptic longitude and latitude (radians)
29423		* @param db double ecliptic longitude and latitude (radians)
29424		*
29425		* <!-- Returned: -->
29426		* @return double ICRS right ascension and declination (radians)
29427		*
29428		*<ol>
29429		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
29430		* convenient way between the two arguments. For example,
29431		* JD(TT)=2450123.7 could be expressed in any of these ways,
29432		* among others:
29433		*
29434		* date1 date2
29435		*
29436		* 2450123.7 0.0 (JD method)
29437		* 2451545.0 -1421.3 (J2000 method)
29438		* 2400000.5 50123.2 (MJD method)
29439		* 2450123.5 0.2 (date & time method)
29440		*
29441		* The JD method is the most natural and convenient to use in
29442		* cases where the loss of several decimal digits of resolution
29443		* is acceptable. The J2000 method is best matched to the way
29444		* the argument is handled internally and will deliver the
29445		* optimum resolution. The MJD method and the date & time methods
29446		* are both good compromises between resolution and convenience.
29447		*
29448		* <li> No assumptions are made about whether the coordinates represent
29449		* starlight and embody astrometric effects such as parallax or
29450		* aberration.
29451		*
29452		* <li> The transformation is approximately that from ecliptic longitude
29453		* and latitude (mean equinox and ecliptic of date) to mean J2000.0
29454		* right ascension and declination, with only frame bias (always
29455		* less than 25 mas) to disturb this classical picture.
29456		*</ol>
29457		* Called: <ul>
29458		* <li>{@link #jauS2c} spherical coordinates to unit vector
29459		* <li>{@link #jauEcm06} J2000.0 to ecliptic rotation matrix, IAU 2006
29460		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
29461		* <li>{@link #jauC2s} unit vector to spherical coordinates
29462		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29463		* <li>{@link #jauAnpm} normalize angle into range +/- pi
29464		*</ul>
29465		*
29466		* @version 2016 February 9
29467		*
29468		* @since JSOFA release 20160503
29469		*
29470		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29471		*/
29472		public static SphericalCoordinate jauEceq06(double date1, double date2, double dl, double db)
29473		{
29474
29475
29476		/* Spherical to Cartesian. */
29477	2	double v1[] = jauS2c(dl, db);
29478
29479		/* Rotation matrix, ICRS equatorial to ecliptic. */
29480	2	double rm[][] = jauEcm06(date1, date2);
29481
29482		/* The transformation from ecliptic to ICRS. */
29483	2	double v2[] = jauTrxp(rm, v1);
29484
29485		/* Cartesian to spherical. */
29486	2	SphericalCoordinate co = jauC2s(v2);
29487
29488		/* Express in conventional ranges. */
29489	2	co.alpha = jauAnp(co.alpha);
29490	2	co.delta = jauAnpm(co.delta);
29491
29492	2	return co;
29493		}
29494
29495		/**
29496		*
29497		* ICRS equatorial to ecliptic rotation matrix, IAU 2006.
29498		*
29499		* <p>This function is derived from the International Astronomical Union's
29500		* SOFA (Standards of Fundamental Astronomy) software collection.
29501		*
29502		* <p>Status: support function.
29503		*
29504		* <!-- Given: -->
29505		* @param date1 double TT as a 2-part Julian date (Note 1)
29506		* @param date2 double TT as a 2-part Julian date (Note 1)
29507		*
29508		* <!-- Returned: -->
29509		* @return double[3][3] ICRS to ecliptic rotation matrix
29510		*
29511		* <p>Notes: <ol>
29512		*
29513		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
29514		* convenient way between the two arguments. For example,
29515		* JD(TT)=2450123.7 could be expressed in any of these ways,
29516		* among others:
29517		*
29518		* date1 date2
29519		*
29520		* 2450123.7 0.0 (JD method)
29521		* 2451545.0 -1421.3 (J2000 method)
29522		* 2400000.5 50123.2 (MJD method)
29523		* 2450123.5 0.2 (date & time method)
29524		*
29525		* The JD method is the most natural and convenient to use in
29526		* cases where the loss of several decimal digits of resolution
29527		* is acceptable. The J2000 method is best matched to the way
29528		* the argument is handled internally and will deliver the
29529		* optimum resolution. The MJD method and the date & time methods
29530		* are both good compromises between resolution and convenience.
29531		*
29532		* <li> The matrix is in the sense
29533		*
29534		* E_ep = rm x P_ICRS,
29535		*
29536		* where P_ICRS is a vector with respect to ICRS right ascension
29537		* and declination axes and E_ep is the same vector with respect to
29538		* the (inertial) ecliptic and equinox of date.
29539		*
29540		* <li> P_ICRS is a free vector, merely a direction, typically of unit
29541		* magnitude, and not bound to any particular spatial origin, such
29542		* as the Earth, Sun or SSB. No assumptions are made about whether
29543		* it represents starlight and embodies astrometric effects such as
29544		* parallax or aberration. The transformation is approximately that
29545		* between mean J2000.0 right ascension and declination and ecliptic
29546		* longitude and latitude, with only frame bias (always less than
29547		* 25 mas) to disturb this classical picture.
29548		* </ol>
29549		* Called: <ul>
29550		* <li>{@link #jauObl06} mean obliquity, IAU 2006
29551		* <li>{@link #jauPmat06} PB matrix, IAU 2006
29552		* <li>{@link #jauIr} initialize r-matrix to identity
29553		* <li>{@link #jauRx} rotate around X-axis
29554		* <li>{@link #jauRxr} product of two r-matrices
29555		*</ul>
29556		*
29557		* @version 2015 December 11
29558		*
29559		* @since JSOFA release 20160503
29560		*
29561		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29562		*/
29563		public static double[][] jauEcm06(double date1, double date2)
29564		{
29565	6	double ob, e[][] = new double[3][3];
29566
29567
29568		/* Obliquity, IAU 2006. */
29569	6	ob = jauObl06(date1, date2);
29570
29571		/* Precession-bias matrix, IAU 2006. */
29572	6	double bp[][] = jauPmat06(date1, date2);
29573
29574		/* Equatorial of date to ecliptic matrix. */
29575	6	jauIr(e);
29576	6	jauRx(ob, e);
29577
29578		/* ICRS to ecliptic coordinates rotation matrix, IAU 2006. */
29579	6	return jauRxr(e, bp);
29580
29581		}
29582
29583		/**
29584		*
29585		* Transformation from ICRS equatorial coordinates to ecliptic
29586		* coordinates (mean equinox and ecliptic of date) using IAU 2006
29587		* precession model.
29588		*
29589		* <p>This function is derived from the International Astronomical Union's
29590		* SOFA (Standards of Fundamental Astronomy) software collection.
29591		*
29592		* <p>Status: support function.
29593		*
29594		* <!-- Given: -->
29595		* @param date1 double TT as a 2-part Julian date (Note 1)
29596		* @param date2 double TT as a 2-part Julian date (Note 1)
29597		* @param dr double ICRS right ascension and declination (radians)
29598		* @param dd double ICRS right ascension and declination (radians)
29599		*
29600		* <!-- Returned: -->
29601		* @return double ecliptic longitude and latitude (radians)
29602		*<ol>
29603		* <li> The TT date date1+date2 is a Julian Date, apportioned in any
29604		* convenient way between the two arguments. For example,
29605		* JD(TT)=2450123.7 could be expressed in any of these ways,
29606		* among others:
29607		*
29608		* date1 date2
29609		*
29610		* 2450123.7 0.0 (JD method)
29611		* 2451545.0 -1421.3 (J2000 method)
29612		* 2400000.5 50123.2 (MJD method)
29613		* 2450123.5 0.2 (date & time method)
29614		*
29615		* The JD method is the most natural and convenient to use in
29616		* cases where the loss of several decimal digits of resolution
29617		* is acceptable. The J2000 method is best matched to the way
29618		* the argument is handled internally and will deliver the
29619		* optimum resolution. The MJD method and the date & time methods
29620		* are both good compromises between resolution and convenience.
29621		*
29622		* <li> No assumptions are made about whether the coordinates represent
29623		* starlight and embody astrometric effects such as parallax or
29624		* aberration.
29625		*
29626		* <li> The transformation is approximately that from mean J2000.0 right
29627		* ascension and declination to ecliptic longitude and latitude
29628		* (mean equinox and ecliptic of date), with only frame bias (always
29629		* less than 25 mas) to disturb this classical picture.
29630		*</ol>
29631		* Called:<ul>
29632		* <li>{@link #jauS2c} spherical coordinates to unit vector
29633		* <li>{@link #jauEcm06} J2000.0 to ecliptic rotation matrix, IAU 2006
29634		* <li>{@link #jauRxp} product of r-matrix and p-vector
29635		* <li>{@link #jauC2s} unit vector to spherical coordinates
29636		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29637		* <li>{@link #jauAnpm} normalize angle into range +/- pi
29638		*</ul>
29639		* @version 2016 February 9
29640		*
29641		* @since JSOFA release 20160503
29642		*
29643		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29644		*/
29645		public static SphericalCoordinate jauEqec06(double date1, double date2, double dr, double dd)
29646		{
29647
29648		/* Spherical to Cartesian. */
29649	2	double v1[] = jauS2c(dr, dd);
29650
29651		/* Rotation matrix, ICRS equatorial to ecliptic. */
29652	2	double rm[][] = jauEcm06(date1, date2);
29653
29654		/* The transformation from ICRS to ecliptic. */
29655	2	double v2[] = jauRxp(rm, v1);
29656
29657		/* Cartesian to spherical. */
29658	2	SphericalCoordinate co = jauC2s(v2);
29659
29660		/* Express in conventional ranges. */
29661	2	co.alpha = jauAnp(co.alpha);
29662	2	co.delta = jauAnpm(co.delta);
29663	2	return co;
29664
29665		}
29666
29667		/**
29668		*
29669		* Transformation from ecliptic coordinates (mean equinox and ecliptic
29670		* of date) to ICRS RA,Dec, using a long-term precession model.
29671		*
29672		* <p>This function is derived from the International Astronomical Union's
29673		* SOFA (Standards of Fundamental Astronomy) software collection.
29674		*
29675		* <p>Status: support function.
29676		*
29677		* <!-- Given: -->
29678		* @param epj double Julian epoch (TT)
29679		* @param dl double ecliptic longitude and latitude (radians)
29680		* @param db double ecliptic longitude and latitude (radians)
29681		*
29682		* <!-- Returned: -->
29683		* @return double ICRS right ascension and declination (radians)
29684		*<ol>
29685		* <li> No assumptions are made about whether the coordinates represent
29686		* starlight and embody astrometric effects such as parallax or
29687		* aberration.
29688		*
29689		* <li> The transformation is approximately that from ecliptic longitude
29690		* and latitude (mean equinox and ecliptic of date) to mean J2000.0
29691		* right ascension and declination, with only frame bias (always
29692		* less than 25 mas) to disturb this classical picture.
29693		*
29694		* <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29695		* agrees with the IAU 2006 precession at J2000.0 and stays within
29696		* 100 microarcseconds during the 20th and 21st centuries. It is
29697		* accurate to a few arcseconds throughout the historical period,
29698		* worsening to a few tenths of a degree at the end of the
29699		* +/- 200,000 year time span.
29700		*</ol>
29701		* Called:<ul>
29702		* <li>{@link #jauS2c} spherical coordinates to unit vector
29703		* <li>{@link #jauLtecm} J2000.0 to ecliptic rotation matrix, long term
29704		* <li>{@link #jauTrxp} product of transpose of r-matrix and p-vector
29705		* <li>{@link #jauC2s} unit vector to spherical coordinates
29706		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29707		* <li>{@link #jauAnpm} normalize angle into range +/- pi
29708		*</ul>
29709		* References: <ul>
29710		*
29711		* <li>Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29712		* expressions, valid for long time intervals, Astron.Astrophys. 534,
29713		* A22
29714		*
29715		* <li>Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29716		* expressions, valid for long time intervals (Corrigendum),
29717		* Astron.Astrophys. 541, C1
29718		*</ul>
29719		* @version 2016 February 9
29720		*
29721		* @since JSOFA release 20160503
29722		*
29723		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29724		*/
29725		public static SphericalCoordinate jauLteceq(double epj, double dl, double db)
29726		{
29727
29728		/* Spherical to Cartesian. */
29729	2	double v1[] = jauS2c(dl, db);
29730
29731		/* Rotation matrix, ICRS equatorial to ecliptic. */
29732	2	double rm[][] = jauLtecm(epj);
29733
29734		/* The transformation from ecliptic to ICRS. */
29735	2	double v2[] = jauTrxp(rm, v1);
29736
29737		/* Cartesian to spherical. */
29738	2	SphericalCoordinate co = jauC2s(v2);
29739
29740		/* Express in conventional ranges. */
29741	2	co.alpha = jauAnp(co.alpha);
29742	2	co.delta = jauAnpm(co.delta);
29743	2	return co;
29744
29745		}
29746
29747		/**
29748		*
29749		* ICRS equatorial to ecliptic rotation matrix, long-term.
29750		*
29751		* <p>This function is derived from the International Astronomical Union's
29752		* SOFA (Standards of Fundamental Astronomy) software collection.
29753		*
29754		* <p>Status: support function.
29755		*
29756		* <!-- Given: -->
29757		* @param epj double Julian epoch (TT)
29758		*
29759		* <!-- Returned: -->
29760		* @return double[3][3] ICRS to ecliptic rotation matrix
29761		*
29762		* <p>Notes: <ol>
29763		*
29764		* <li> The matrix is in the sense
29765		*
29766		* E_ep = rm x P_ICRS,
29767		*
29768		* where P_ICRS is a vector with respect to ICRS right ascension
29769		* and declination axes and E_ep is the same vector with respect to
29770		* the (inertial) ecliptic and equinox of epoch epj.
29771		*
29772		* <li> P_ICRS is a free vector, merely a direction, typically of unit
29773		* magnitude, and not bound to any particular spatial origin, such
29774		* as the Earth, Sun or SSB. No assumptions are made about whether
29775		* it represents starlight and embodies astrometric effects such as
29776		* parallax or aberration. The transformation is approximately that
29777		* between mean J2000.0 right ascension and declination and ecliptic
29778		* longitude and latitude, with only frame bias (always less than
29779		* 25 mas) to disturb this classical picture.
29780		*
29781		* <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29782		* agrees with the IAU 2006 precession at J2000.0 and stays within
29783		* 100 microarcseconds during the 20th and 21st centuries. It is
29784		* accurate to a few arcseconds throughout the historical period,
29785		* worsening to a few tenths of a degree at the end of the
29786		* +/- 200,000 year time span.
29787		*</ol>
29788		* Called:<ul>
29789		* <li>{@link #jauLtpequ} equator pole, long term
29790		* <li>{@link #jauLtpecl} ecliptic pole, long term
29791		* <li>{@link #jauPxp} vector product
29792		* <li>{@link #jauPn} normalize vector
29793		*</ul>
29794		* References:<ul>
29795		*
29796		* <li>Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29797		* expressions, valid for long time intervals, Astron.Astrophys. 534,
29798		* A22
29799		*
29800		* <li>Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29801		* expressions, valid for long time intervals (Corrigendum),
29802		* Astron.Astrophys. 541, C1
29803		*</ul>
29804		* @version 2015 December 6
29805		*
29806		* @since JSOFA release 20160503
29807		*
29808		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29809		*/
29810		public static double[][] jauLtecm(double epj)
29811		{
29812	6	double rm[][] = new double[3][3];
29813		/* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
29814	6	final double dx = -0.016617 * DAS2R,
29815	6	de = -0.0068192 * DAS2R,
29816	6	dr = -0.0146 * DAS2R;
29817
29818
29819		/* Equator pole. */
29820	6	double p[] = jauLtpequ(epj);
29821
29822		/* Ecliptic pole (bottom row of equatorial to ecliptic matrix). */
29823	6	double z[] = jauLtpecl(epj);
29824
29825		/* Equinox (top row of matrix). */
29826	6	double w[] = jauPxp(p, z);
29827	6	NormalizedVector nv = jauPn(w);
29828
29829	6	double x[] = nv.u;
29830		/* Middle row of matrix. */
29831	6	double y[] = jauPxp(z, x);
29832
29833		/* Combine with frame bias. */
29834	6	rm[0][0] = x[0] - x[1]dr + x[2]dx;
29835	6	rm[0][1] = x[0]dr + x[1] + x[2]de;
29836	6	rm[0][2] = - x[0]dx - x[1]de + x[2];
29837	6	rm[1][0] = y[0] - y[1]dr + y[2]dx;
29838	6	rm[1][1] = y[0]dr + y[1] + y[2]de;
29839	6	rm[1][2] = - y[0]dx - y[1]de + y[2];
29840	6	rm[2][0] = z[0] - z[1]dr + z[2]dx;
29841	6	rm[2][1] = z[0]dr + z[1] + z[2]de;
29842	6	rm[2][2] = - z[0]dx - z[1]de + z[2];
29843
29844	6	return rm;
29845
29846		}
29847
29848		/**
29849		*
29850		* Transformation from ICRS equatorial coordinates to ecliptic
29851		* coordinates (mean equinox and ecliptic of date) using a long-term
29852		* precession model.
29853		*
29854		* <p>This function is derived from the International Astronomical Union's
29855		* SOFA (Standards of Fundamental Astronomy) software collection.
29856		*
29857		* <p>Status: support function.
29858		*
29859		* <!-- Given: -->
29860		* @param epj double Julian epoch (TT)
29861		* @param dr,dd double ICRS right ascension and declination (radians)
29862		*
29863		* <!-- Returned: -->
29864		* @return ecliptic longitude and latitude (radians)
29865		*<ol>
29866		* <li> No assumptions are made about whether the coordinates represent
29867		* starlight and embody astrometric effects such as parallax or
29868		* aberration.
29869		*
29870		* <li> The transformation is approximately that from mean J2000.0 right
29871		* ascension and declination to ecliptic longitude and latitude
29872		* (mean equinox and ecliptic of date), with only frame bias (always
29873		* less than 25 mas) to disturb this classical picture.
29874		*
29875		* <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29876		* agrees with the IAU 2006 precession at J2000.0 and stays within
29877		* 100 microarcseconds during the 20th and 21st centuries. It is
29878		* accurate to a few arcseconds throughout the historical period,
29879		* worsening to a few tenths of a degree at the end of the
29880		* +/- 200,000 year time span.
29881		*</ol>
29882		* Called:<ul>
29883		* <li>{@link #jauS2c} spherical coordinates to unit vector
29884		* <li>{@link #jauLtecm} J2000.0 to ecliptic rotation matrix, long term
29885		* <li>{@link #jauRxp} product of r-matrix and p-vector
29886		* <li>{@link #jauC2s} unit vector to spherical coordinates
29887		* <li>{@link #jauAnp} normalize angle into range 0 to 2pi
29888		* <li>{@link #jauAnpm} normalize angle into range +/- pi
29889		*</ul>
29890		* References:
29891		*
29892		* Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29893		* expressions, valid for long time intervals, Astron.Astrophys. 534,
29894		* A22
29895		*
29896		* Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29897		* expressions, valid for long time intervals (Corrigendum),
29898		* Astron.Astrophys. 541, C1
29899		*
29900		* @version 2016 February 9
29901		*
29902		* @since JSOFA release 20160503
29903		*
29904		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29905		*/
29906		public static SphericalCoordinate jauLteqec(double epj, double dr, double dd)
29907		{
29908
29909		/* Spherical to Cartesian. */
29910	2	double v1[] = jauS2c(dr, dd);
29911
29912		/* Rotation matrix, ICRS equatorial to ecliptic. */
29913	2	double rm[][] = jauLtecm(epj);
29914
29915		/* The transformation from ICRS to ecliptic. */
29916	2	double v2[] = jauRxp(rm, v1);
29917
29918		/* Cartesian to spherical. */
29919	2	SphericalCoordinate co = jauC2s(v2);
29920
29921		/* Express in conventional ranges. */
29922	2	co.alpha = jauAnp(co.alpha);
29923	2	co.delta = jauAnpm(co.delta);
29924
29925	2	return co;
29926		}
29927
29928		/**
29929		*
29930		* Long-term precession matrix.
29931		*
29932		* <p>This function is derived from the International Astronomical Union's
29933		* SOFA (Standards of Fundamental Astronomy) software collection.
29934		*
29935		* <p>Status: support function.
29936		*
29937		* <!-- Given: -->
29938		* @param epj double Julian epoch (TT)
29939		*
29940		* <!-- Returned: -->
29941		* @return double[3][3] precession matrix, J2000.0 to date
29942		*
29943		* <p>Notes: <ol>
29944		*
29945		* <li> The matrix is in the sense
29946		*
29947		* P_date = rp x P_J2000,
29948		*
29949		* where P_J2000 is a vector with respect to the J2000.0 mean
29950		* equator and equinox and P_date is the same vector with respect to
29951		* the equator and equinox of epoch epj.
29952		*
29953		* <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
29954		* agrees with the IAU 2006 precession at J2000.0 and stays within
29955		* 100 microarcseconds during the 20th and 21st centuries. It is
29956		* accurate to a few arcseconds throughout the historical period,
29957		* worsening to a few tenths of a degree at the end of the
29958		* +/- 200,000 year time span.
29959		*</ol>
29960		* Called:<ul>
29961		* <li>{@link #jauLtpequ} equator pole, long term
29962		* <li>{@link #jauLtpecl} ecliptic pole, long term
29963		* <li>{@link #jauPxp} vector product
29964		* <li>{@link #jauPn} normalize vector
29965		*</ul>
29966		* References:
29967		*
29968		* <p>Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
29969		* expressions, valid for long time intervals, Astron.Astrophys. 534,
29970		* A22
29971		*
29972		* <p>Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
29973		* expressions, valid for long time intervals (Corrigendum),
29974		* Astron.Astrophys. 541, C1
29975		*
29976		* @version 2015 December 6
29977		*
29978		* @since JSOFA release 20160503
29979		*
29980		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
29981		*/
29982		public static double[][] jauLtp(double epj )
29983		{
29984	4	double rp[][] = new double[3][3];
29985		int i;
29986
29987
29988
29989		/* Equator pole (bottom row of matrix). */
29990	4	double peqr[] = jauLtpequ(epj);
29991
29992		/* Ecliptic pole. */
29993	4	double pecl[] = jauLtpecl(epj);
29994
29995		/* Equinox (top row of matrix). */
29996	4	double v[] = jauPxp(peqr, pecl);
29997	4	NormalizedVector nv = jauPn(v);
29998
29999		/* Middle row of matrix. */
30000	4	v = jauPxp(peqr, nv.u);
30001
30002		/* Assemble the matrix. */
30003	16	for ( i = 0; i < 3; i++ ) {
30004	12	rp[0][i] = nv.u[i];
30005	12	rp[1][i] = v[i];
30006	12	rp[2][i] = peqr[i];
30007		}
30008
30009	4	return rp;
30010		}
30011
30012
30013		/**
30014		*
30015		* Long-term precession matrix, including ICRS frame bias.
30016		*
30017		* <p>This function is derived from the International Astronomical Union's
30018		* SOFA (Standards of Fundamental Astronomy) software collection.
30019		*
30020		* <p>Status: support function.
30021		*
30022		* <!-- Given: -->
30023		* @param epj double Julian epoch (TT)
30024		*
30025		* <!-- Returned: -->
30026		* @return double[3][3] precession-bias matrix, J2000.0 to date
30027		*
30028		* <p>Notes: <ol>
30029		*
30030		* <li> The matrix is in the sense
30031		*
30032		* P_date = rpb x P_ICRS,
30033		*
30034		* where P_ICRS is a vector in the Geocentric Celestial Reference
30035		* System, and P_date is the vector with respect to the Celestial
30036		* Intermediate Reference System at that date but with nutation
30037		* neglected.
30038		*
30039		* <li> A first order frame bias formulation is used, of sub-
30040		* microarcsecond accuracy compared with a full 3D rotation.
30041		*
30042		* <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
30043		* agrees with the IAU 2006 precession at J2000.0 and stays within
30044		* 100 microarcseconds during the 20th and 21st centuries. It is
30045		* accurate to a few arcseconds throughout the historical period,
30046		* worsening to a few tenths of a degree at the end of the
30047		* +/- 200,000 year time span.
30048		*</ol>
30049		* References:
30050		*
30051		* Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
30052		* expressions, valid for long time intervals, Astron.Astrophys. 534,
30053		* A22
30054		*
30055		* Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
30056		* expressions, valid for long time intervals (Corrigendum),
30057		* Astron.Astrophys. 541, C1
30058		*
30059		* @version 2015 December 6
30060		*
30061		* @since JSOFA release 20160503
30062		*
30063		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
30064		*/
30065		public static double[][] jauLtpb(double epj)
30066		{
30067	2	double rpb[][] = new double[3][3];
30068		/* Frame bias (IERS Conventions 2010, Eqs. 5.21 and 5.33) */
30069	2	final double dx = -0.016617 * DAS2R,
30070	2	de = -0.0068192 * DAS2R,
30071	2	dr = -0.0146 * DAS2R;
30072
30073		int i;
30074
30075
30076
30077		/* Precession matrix. */
30078	2	double rp[][] = jauLtp(epj);
30079
30080		/* Apply the bias. */
30081	8	for ( i = 0; i < 3; i++ ) {
30082	6	rpb[i][0] = rp[i][0] - rp[i][1]dr + rp[i][2]dx;
30083	6	rpb[i][1] = rp[i][0]dr + rp[i][1] + rp[i][2]de;
30084	6	rpb[i][2] = -rp[i][0]dx - rp[i][1]de + rp[i][2];
30085		}
30086
30087	2	return rpb;
30088		}
30089
30090		/**
30091		*
30092		* Long-term precession of the ecliptic.
30093		*
30094		* <p>This function is derived from the International Astronomical Union's
30095		* SOFA (Standards of Fundamental Astronomy) software collection.
30096		*
30097		* <p>Status: support function.
30098		*
30099		* <!-- Given: -->
30100		* @param epj double Julian epoch (TT)
30101		*
30102		* <!-- Returned: -->
30103		* @return double[3] ecliptic pole unit vector
30104		*
30105		* <p>Notes: <ol>
30106		*
30107		* <li> The returned vector is with respect to the J2000.0 mean equator
30108		* and equinox.
30109		*
30110		* <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
30111		* agrees with the IAU 2006 precession at J2000.0 and stays within
30112		* 100 microarcseconds during the 20th and 21st centuries. It is
30113		* accurate to a few arcseconds throughout the historical period,
30114		* worsening to a few tenths of a degree at the end of the
30115		* +/- 200,000 year time span.
30116		*</ol>
30117		* References:
30118		*
30119		* Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
30120		* expressions, valid for long time intervals, Astron.Astrophys. 534,
30121		* A22
30122		*
30123		* Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
30124		* expressions, valid for long time intervals (Corrigendum),
30125		* Astron.Astrophys. 541, C1
30126		*
30127		* @version 2016 February 9
30128		*
30129		* @since JSOFA release 20160503
30130		*
30131		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
30132		*/
30133		public static double[] jauLtpecl(double epj)
30134		{
30135
30136	12	double vec[] = new double[3];
30137		/* Obliquity at J2000.0 (radians). */
30138	12	final double eps0 = 84381.406 * DAS2R;
30139
30140		/* Polynomial coefficients */
30141	12	final int NPOL = 4 ;
30142	12	final double pqpol[][] = {
30143		{ 5851.607687,
30144		-0.1189000,
30145		-0.00028913,
30146		0.000000101},
30147		{-1600.886300,
30148		1.1689818,
30149		-0.00000020,
30150		-0.000000437}
30151		};
30152
30153		/* Periodic coefficients */
30154	12	final double pqper[][] = {
30155		{ 708.15,-5486.751211,-684.661560, 667.666730,-5523.863691},
30156		{2309.00, -17.127623,2446.283880,-2354.886252, -549.747450},
30157		{1620.00, -617.517403, 399.671049, -428.152441, -310.998056},
30158		{ 492.20, 413.442940,-356.652376, 376.202861, 421.535876},
30159		{1183.00, 78.614193,-186.387003, 184.778874, -36.776172},
30160		{ 622.00, -180.732815,-316.800070, 335.321713, -145.278396},
30161		{ 882.00, -87.676083, 198.296701, -185.138669, -34.744450},
30162		{ 547.00, 46.140315, 101.135679, -120.972830, 22.885731}
30163		};
30164	12	final int NPER = pqper.length;
30165
30166		/* Miscellaneous */
30167		int i;
30168		double t, p, q, w, a, s, c;
30169
30170
30171		/* Centuries since J2000. */
30172	12	t = ( epj - 2000.0 ) / 100.0;
30173
30174		/* Initialize P_A and Q_A accumulators. */
30175	12	p = 0.0;
30176	12	q = 0.0;
30177
30178		/* Periodic terms. */
30179	12	w = D2PI*t;
30180	108	for ( i = 0; i < NPER; i++ ) {
30181	96	a = w/pqper[i][0];
30182	96	s = sin(a);
30183	96	c = cos(a);
30184	96	p += cpqper[i][1] + spqper[i][3];
30185	96	q += cpqper[i][2] + spqper[i][4];
30186		}
30187
30188		/* Polynomial terms. */
30189	12	w = 1.0;
30190	60	for ( i = 0; i < NPOL; i++ ) {
30191	48	p += pqpol[0][i]*w;
30192	48	q += pqpol[1][i]*w;
30193	48	w *= t;
30194		}
30195
30196		/* P_A and Q_A (radians). */
30197	12	p *= DAS2R;
30198	12	q *= DAS2R;
30199
30200		/* Form the ecliptic pole vector. */
30201	12	w = 1.0 - pp - qq;
30202	12	w = w < 0.0 ? 0.0 : sqrt(w);
30203	12	s = sin(eps0);
30204	12	c = cos(eps0);
30205	12	vec[0] = p;
30206	12	vec[1] = - qc - ws;
30207	12	vec[2] = - qs + wc;
30208
30209	12	return vec;
30210
30211		}
30212
30213		/**
30214		*
30215		* Long-term precession of the equator.
30216		*
30217		* <p>This function is derived from the International Astronomical Union's
30218		* SOFA (Standards of Fundamental Astronomy) software collection.
30219		*
30220		* <p>Status: support function.
30221		*
30222		* <!-- Given: -->
30223		* @param epj double Julian epoch (TT)
30224		*
30225		* <!-- Returned: -->
30226		* @return double[3] equator pole unit vector
30227		*
30228		* <p>Notes: <ol>
30229		*
30230		* <li> The returned vector is with respect to the J2000.0 mean equator
30231		* and equinox.
30232		*
30233		* <li> The Vondrak et al. (2011, 2012) 400 millennia precession model
30234		* agrees with the IAU 2006 precession at J2000.0 and stays within
30235		* 100 microarcseconds during the 20th and 21st centuries. It is
30236		* accurate to a few arcseconds throughout the historical period,
30237		* worsening to a few tenths of a degree at the end of the
30238		* +/- 200,000 year time span.
30239		*</ol>
30240		* References:
30241		*
30242		* Vondrak, J., Capitaine, N. and Wallace, P., 2011, New precession
30243		* expressions, valid for long time intervals, Astron.Astrophys. 534,
30244		* A22
30245		*
30246		* Vondrak, J., Capitaine, N. and Wallace, P., 2012, New precession
30247		* expressions, valid for long time intervals (Corrigendum),
30248		* Astron.Astrophys. 541, C1
30249		*
30250		* @version 2016 February 9
30251		*
30252		* @since JSOFA release 20160503
30253		*
30254		* <!--Copyright (C) 2016 IAU SOFA Board. See notes at end. -->
30255		*/
30256		public static double[] jauLtpequ(double epj)
30257		{
30258	12	double veq[] = new double[3];
30259		/* Polynomial coefficients */
30260	12	final int NPOL = 4;
30261	12	final double xypol[][] = {
30262		{ 5453.282155,
30263		0.4252841,
30264		-0.00037173,
30265		-0.000000152},
30266		{-73750.930350,
30267		-0.7675452,
30268		-0.00018725,
30269		0.000000231}
30270		};
30271
30272		/* Periodic coefficients */
30273	12	final double xyper[][] = {
30274		{ 256.75, -819.940624,75004.344875,81491.287984, 1558.515853},
30275		{ 708.15,-8444.676815, 624.033993, 787.163481, 7774.939698},
30276		{ 274.20, 2600.009459, 1251.136893, 1251.296102,-2219.534038},
30277		{ 241.45, 2755.175630,-1102.212834,-1257.950837,-2523.969396},
30278		{2309.00, -167.659835,-2660.664980,-2966.799730, 247.850422},
30279		{ 492.20, 871.855056, 699.291817, 639.744522, -846.485643},
30280		{ 396.10, 44.769698, 153.167220, 131.600209,-1393.124055},
30281		{ 288.90, -512.313065, -950.865637, -445.040117, 368.526116},
30282		{ 231.10, -819.415595, 499.754645, 584.522874, 749.045012},
30283		{1610.00, -538.071099, -145.188210, -89.756563, 444.704518},
30284		{ 620.00, -189.793622, 558.116553, 524.429630, 235.934465},
30285		{ 157.87, -402.922932, -23.923029, -13.549067, 374.049623},
30286		{ 220.30, 179.516345, -165.405086, -210.157124, -171.330180},
30287		{1200.00, -9.814756, 9.344131, -44.919798, -22.899655}
30288		};
30289	12	final int NPER = xyper.length;
30290
30291		/* Miscellaneous */
30292		int i;
30293		double t, x, y, w, a, s, c;
30294
30295
30296		/* Centuries since J2000. */
30297	12	t = ( epj - 2000.0 ) / 100.0;
30298
30299		/* Initialize X and Y accumulators. */
30300	12	x = 0.0;
30301	12	y = 0.0;
30302
30303		/* Periodic terms. */
30304	12	w = D2PI * t;
30305	180	for ( i = 0; i < NPER; i++ ) {
30306	168	a = w / xyper[i][0];
30307	168	s = sin(a);
30308	168	c = cos(a);
30309	168	x += cxyper[i][1] + sxyper[i][3];
30310	168	y += cxyper[i][2] + sxyper[i][4];
30311		}
30312
30313		/* Polynomial terms. */
30314	12	w = 1.0;
30315	60	for ( i = 0; i < NPOL; i++ ) {
30316	48	x += xypol[0][i]*w;
30317	48	y += xypol[1][i]*w;
30318	48	w *= t;
30319		}
30320
30321		/* X and Y (direction cosines). */
30322	12	x *= DAS2R;
30323	12	y *= DAS2R;
30324
30325		/* Form the equator pole vector. */
30326	12	veq[0] = x;
30327	12	veq[1] = y;
30328	12	w = 1.0 - xx - yy;
30329	12	veq[2] = w < 0.0 ? 0.0 : sqrt(w);
30330
30331
30332	12	return veq;
30333
30334		}
30335
30336		}
30337
30338		/*
30339		* Copyright © 2016 Paul Harrison, University of Manchester.
30340		*
30341		* This JSOFA software is derived from the official C release of the "Standards Of Fundamental Astronomy" (SOFA) library
30342		* of the International Astronomical Union. The intention is to reproduce the functionality and algorithms of
30343		* the official SOFA library in a pure Java form.
30344		*
30345		* The responsibility for the maintenance and supply of the JSOFA library lies with the author (not the IAU SOFA Board),
30346		* However, The JSOFA software is provided "as is" and the author makes no warranty as to its use or performance.
30347		* The author does not and cannot warrant the performance or results which the user may obtain by using the JSOFA software.
30348		* The author makes no warranties, express or implied, as to non-infringement of third party rights, merchantability,
30349		* or fitness for any particular purpose. In no event will the author be liable to the user for any consequential,
30350		* incidental, or special damages, including any lost profits or lost savings, even if the author has been advised
30351		* of such damages, or for any claim by any third party.
30352		*
30353		* Other conditions of the original license (reproduced below) are carried over as applicable.
30354		*/
30355
30356		/*----------------------------------------------------------------------
30357		**
30358		** Copyright (C) 2016
30359		** Standards Of Fundamental Astronomy Board
30360		** of the International Astronomical Union.
30361		**
30362		** =====================
30363		** SOFA Software License
30364		** =====================
30365		**
30366		** NOTICE TO USER:
30367		**
30368		** BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING SIX TERMS AND
30369		** CONDITIONS WHICH APPLY TO ITS USE.
30370		**
30371		** 1. The Software is owned by the IAU SOFA Board ("SOFA").
30372		**
30373		** 2. Permission is granted to anyone to use the SOFA software for any
30374		** purpose, including commercial applications, free of charge and
30375		** without payment of royalties, subject to the conditions and
30376		** restrictions listed below.
30377		**
30378		** 3. You (the user) may copy and distribute SOFA source code to others,
30379		** and use and adapt its code and algorithms in your own software,
30380		** on a world-wide, royalty-free basis. That portion of your
30381		** distribution that does not consist of intact and unchanged copies
30382		** of SOFA source code files is a "derived work" that must comply
30383		** with the following requirements:
30384		**
30385		** a) Your work shall be marked or carry a statement that it
30386		** (i) uses routines and computations derived by you from
30387		** software provided by SOFA under license to you; and
30388		** (ii) does not itself constitute software provided by and/or
30389		** endorsed by SOFA.
30390		**
30391		** b) The source code of your derived work must contain descriptions
30392		** of how the derived work is based upon, contains and/or differs
30393		** from the original SOFA software.
30394		**
30395		** c) The names of all routines in your derived work shall not
30396		** include the prefix "iau" or "sofa" or trivial modifications
30397		** thereof such as changes of case.
30398		**
30399		** d) The origin of the SOFA components of your derived work must
30400		** not be misrepresented; you must not claim that you wrote the
30401		** original software, nor file a patent application for SOFA
30402		** software or algorithms embedded in the SOFA software.
30403		**
30404		** e) These requirements must be reproduced intact in any source
30405		** distribution and shall apply to anyone to whom you have
30406		** granted a further right to modify the source code of your
30407		** derived work.
30408		**
30409		** Note that, as originally distributed, the SOFA software is
30410		** intended to be a definitive implementation of the IAU standards,
30411		** and consequently third-party modifications are discouraged. All
30412		** variations, no matter how minor, must be explicitly marked as
30413		** such, as explained above.
30414		**
30415		** 4. You shall not cause the SOFA software to be brought into
30416		** disrepute, either by misuse, or use for inappropriate tasks, or
30417		** by inappropriate modification.
30418		**
30419		** 5. The SOFA software is provided "as is" and SOFA makes no warranty
30420		** as to its use or performance. SOFA does not and cannot warrant
30421		** the performance or results which the user may obtain by using the
30422		** SOFA software. SOFA makes no warranties, express or implied, as
30423		** to non-infringement of third party rights, merchantability, or
30424		** fitness for any particular purpose. In no event will SOFA be
30425		** liable to the user for any consequential, incidental, or special
30426		** damages, including any lost profits or lost savings, even if a
30427		** SOFA representative has been advised of such damages, or for any
30428		** claim by any third party.
30429		**
30430		** 6. The provision of any version of the SOFA software under the terms
30431		** and conditions specified herein does not imply that future
30432		** versions will also be made available under the same terms and
30433		** conditions.
30434		*
30435		** In any published work or commercial product which uses the SOFA
30436		** software directly, acknowledgement (see www.iausofa.org) is
30437		** appreciated.
30438		**
30439		** Correspondence concerning SOFA software should be addressed as
30440		** follows:
30441		**
30442		** By email: sofa@ukho.gov.uk
30443		** By post: IAU SOFA Center
30444		** HM Nautical Almanac Office
30445		** UK Hydrographic Office
30446		** Admiralty Way, Taunton
30447		** Somerset, TA1 2DN
30448		** United Kingdom
30449		**
30450		*--------------------------------------------------------------------/
30451
30452
30453		/*
30454		* $Log$
30455		*/